18. Q18
Save videos to My Cheatsheet for later, for easy studying.
Video Solution
Q1
Q2
Q3
L1
L2
L3
Similar Question 1
<p>Verify that <code class='latex inline'>QS</code> does not bisect <code class='latex inline'>PR</code>.</p><img src="/qimages/744" />
Similar Question 2
<p>Use analytic geometry to verify that</p><p><strong>(a)</strong> Draw the trapezoid with vertices <code class='latex inline'>A(-2, -2), B(2, -2), C(4, 1)</code>, and <code class='latex inline'>D(2, 4)</code>.</p><p><strong>(b)</strong> Verify that the line segment joining the midpoints of the non-parallel sides of the trapezoid is parallel to the other two sides.</p>
Similar Question 3
<p>Which of the <code class='latex inline'>A(-4,3)</code> and <code class='latex inline'>B(3,-4)</code> </p><p>lie on <code class='latex inline'>x^2+y^2=25</code>?</p>
Similar Questions
Learning Path
L1 Quick Intro to Factoring Trinomial with Leading a
L2 Introduction to Factoring ax^2+bx+c
L3 Factoring ax^2+bx+c, ex1
Now You Try
<p>What are the slopes of the diagonals of quadrilateral <code class='latex inline'>JKLM</code>. Are they perpendicular?</p><img src="/qimages/718" />
<p>Which of the line segments inside each quadrilateral are parallel?</p><img src="/qimages/737" />
<p>Verify that the diagonals of <code class='latex inline'>ABCD</code> are equal in length and bisect each other.</p><img src="/qimages/743" />
<p>A triangle has vertices at <code class='latex inline'>D(-5,4), E(1,8),</code> and <code class='latex inline'>F(-1,-2)</code>. </p><p>a) Find the Mid Point of <code class='latex inline'>EF</code> say M.</p><p>b) Determine the slope of <code class='latex inline'>MD</code> and <code class='latex inline'>EF</code></p><p>c) The result from part b) tell us that?</p>
<p><strong>(a)</strong> Draw the quadrilateral with vertices <code class='latex inline'>A(3, 4), B(-1, 2), C(-3, -4)</code>, and <code class='latex inline'>D(5, -6)</code>. Then, join the midpoints of the adjacent sides of <code class='latex inline'>ABCD</code> to form a new quadrilateral, <code class='latex inline'>EFGH</code>.</p><p><strong>(b)</strong> Verify that <code class='latex inline'>EFGH</code> is a rhombus.</p>
<p>Find the slopes for the line segment joining points <code class='latex inline'>P(1, 4)</code> and <code class='latex inline'>Q6, 5)</code> and line segment joining points <code class='latex inline'>R(3, -4)</code> and <code class='latex inline'>S(7, -3)</code>.</p>
<p>Verify that <code class='latex inline'>ST</code> is parallel to <code class='latex inline'>QR</code> where <code class='latex inline'>P(-12, 6), Q(4, 0)</code>, and <code class='latex inline'>R(-8, -6)</code>.</p>
<p>What kind of shape does the mid-segments of a rhombus with vertices at <code class='latex inline'>R(-5,2), S(-1,3), T(-2,-1)</code> and <code class='latex inline'>U(-6,-2)</code> form?</p>
<p> Verify that quadrilateral <code class='latex inline'>ABCD</code> is a trapezoid.</p><img src="/qimages/740" />
<p>A quadrilateral has vertices <code class='latex inline'>P(-5, 4), Q(-2, 8), R(6, 2)</code> and <code class='latex inline'>S(3, -2)</code>.</p> <ul> <li>Show that the quadrilateral is a rectangle</li> </ul>
<p>Verify that <code class='latex inline'>QS</code> does not bisect <code class='latex inline'>PR</code>.</p><img src="/qimages/744" />
<p>How are <code class='latex inline'>\angle BAD</code> and <code class='latex inline'>\angle BCD</code> related?</p><img src="/qimages/745" />
<p>A rectangle has vertices at <code class='latex inline'>A(-6,5), B(12,-1), C(8,-13),</code> and <code class='latex inline'>D(-10,-7)</code>. Show that the diagonals are the same length.</p>
<p><strong>(d)</strong> Verify that opposite sides of TUVW are equal in length.</p><p>Below was Question a), b), and c) <code class='latex inline'>\to</code></p> <ul> <li><strong>(a)</strong> Draw the quadrilateral with vertices <code class='latex inline'>P(0, 7), Q(-2, 1), R(4, -1)</code>, and <code class='latex inline'>S(6, 3)</code>.</li> <li><strong>(b)</strong> Find the midpoint of each side. Join the midpoints of adjacent sides to form a new quadrilateral <code class='latex inline'>TUVW</code>.</li> <li><strong>(c)</strong> Verify that opposite sides of <code class='latex inline'>TUVW</code> are parallel.</li> </ul>
<p>A quadrilateral has vertices <code class='latex inline'>O(0, 0), P(3, 5), Q(8, 6)</code>, and <code class='latex inline'>R(5, 1)</code>.</p><p><strong>(a)</strong> Determine whether OPQR is a parallelogram.</p><p><strong>(b)</strong> Describe how you could use geometry software to verify your answer to part (a).</p>
<p>A quadrilateral has vertices <code class='latex inline'>P(-5, 4), Q(-2, 8), R(6, 2)</code> and <code class='latex inline'>S(3, -2)</code>.</p> <ul> <li>Determine the length of each diagonal.</li> </ul>
<p><strong>(c)</strong> Verify that opposite sides of <code class='latex inline'>TUVW</code> are parallel.</p><p>Below was Question a) and b) <code class='latex inline'>\to</code></p> <ul> <li><strong>(a)</strong> Draw the quadrilateral with vertices <code class='latex inline'>P(0, 7), Q(-2, 1), R(4, -1)</code>, and <code class='latex inline'>S(6, 3)</code>.</li> <li><strong>(b)</strong> Find the midpoint of each side. Join the midpoints of adjacent sides to form a new quadrilateral <code class='latex inline'>TUVW</code>.</li> </ul>
<p>Which of the line segments inside each quadrilateral are parallel?</p><img src="/qimages/736" />
<p> <code class='latex inline'>A(-4,3)</code> and <code class='latex inline'>B(3,-4)</code> lie on <code class='latex inline'>x^2+y^2=25</code>. </p><p>The perpendicular bisector of chord <code class='latex inline'>AB</code>, does it passes through the centre of the circle? Show your work.</p>
<p>Nina claims that the midpoint of the hypotenuse of a right triangle is the same distance from each vertex of the triangle. Create flow chart that summarizes the steps you would take to verify this property.</p>
<p>A polygon is defined by points <code class='latex inline'>R(-5, 1), 5(5, 3), T(2, -1)</code>, and <code class='latex inline'>U(-8, -3)</code>. Categorize this polygon.</p>
<p>A rectangle has vertices at <code class='latex inline'>J(10,0), K(-8,6), L(-12,-6),</code> and <code class='latex inline'>M(6,-12)</code>. Show that the diagonals bisect each other by finding the midpoint between <code class='latex inline'>JL</code> and <code class='latex inline'>KM</code>.</p>
<p>The mid-segments of a square with vertices at <code class='latex inline'>A(2, - 12), B(- 10, -8), C(-6, 4)</code>, and <code class='latex inline'>D(6, 0)</code> form which of the following shapes?</p>
<p>Do all rectangles have this property?</p>
<p>Find the length of <code class='latex inline'>FH</code>.</p><img src="/qimages/738" />
<p>Verify that quadrilateral <code class='latex inline'>EFGH</code> is a rhombus.</p><img src="/qimages/741" />
<p> A quadrilateral has vertices at <code class='latex inline'>A(-2, 3), B(-2, -2), C(2, 1)</code>, and <code class='latex inline'>D(2, 6)</code>. Show that the quadrilateral is a rhombus.</p>
<p>A quadrilateral has vertices <code class='latex inline'>P(-5, 4), Q(-2, 8), R(6, 2)</code> and <code class='latex inline'>S(3, -2)</code>.</p> <ul> <li>(a) Determine the midpoint of each diagonal.</li> <li>(b) What can you conclude about the diagonals of PQRS?</li> </ul>
<p>Verify that quadrilateral <code class='latex inline'>ABCD</code> is a rectangle.</p><img src="/qimages/743" />
<p>Use analytic geometry to verify that</p><p><strong>(a)</strong> Draw the trapezoid with vertices <code class='latex inline'>A(-2, -2), B(2, -2), C(4, 1)</code>, and <code class='latex inline'>D(2, 4)</code>.</p><p><strong>(b)</strong> Verify that the line segment joining the midpoints of the non-parallel sides of the trapezoid is parallel to the other two sides.</p>
<p>For <code class='latex inline'>A(3, 4), B(-1, 2), C(-3, -4)</code>, and <code class='latex inline'>D(5, -6)</code>, midpoints of the adjacent sides of <code class='latex inline'>ABCD</code> to form a new quadrilateral, <code class='latex inline'>EFGH</code>.</p><p>Describe another method for verifying that EFGH is a rhombus.</p><img src="/qimages/1688" />
<p>What can you conclude about the lengths of the sides of <code class='latex inline'>JKLM</code>? Explain your reasoning.</p>
<p>Verify that <code class='latex inline'>PR</code> bisects <code class='latex inline'>QS</code> at right angles.</p><img src="/qimages/744" />
<p>Which of the line segments inside each parallelogram are equal in length?</p><img src="/qimages/735" />
<p><strong>(a)</strong> Draw the quadrilateral with vertices <code class='latex inline'>P(0, 7), Q(-2, 1), R(4, -1)</code>, and <code class='latex inline'>S(6, 3)</code>.</p><p><strong>(b)</strong> Find the midpoint of each side. Join the midpoints of adjacent sides to form a new quadrilateral <code class='latex inline'>TUVW</code>.</p>
<p>Which of the <code class='latex inline'>A(-4,3)</code> and <code class='latex inline'>B(3,-4)</code> </p><p>lie on <code class='latex inline'>x^2+y^2=25</code>?</p>
<p>A trapezoid has vertices at <code class='latex inline'>A(1,2), B(-2,1), C(-4,-2),</code> and <code class='latex inline'>D(2,0)</code>.</p> <ul> <li>Show that the sum length of line formed with midpoint of BC and AD is half the sum of the lengths of the parallel sides.</li> </ul>
<p><code class='latex inline'>\triangle PQR</code> has vertices at <code class='latex inline'>P(-2,1), Q(1,5),</code> and <code class='latex inline'>R(5,2)</code>. Show that the median from vertex <code class='latex inline'>Q</code> is the perpendicular bisector of <code class='latex inline'>PR</code> by finding the slope of median from <code class='latex inline'>Q</code> and slope of <code class='latex inline'>PR</code>.</p>
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(3, 4), B(-2, 0)</code>, and <code class='latex inline'>C(5, 0)</code>. Prove that the area of the triangle formed by joining the midpoints of <code class='latex inline'>\triangle ABC</code> is one-quarter the area of <code class='latex inline'>\triangle ABC</code>.</p>
<p>Find the lengths of the mid-segments of a quadrilateral with vertices at <code class='latex inline'>P(-2, -2), Q(0, 4), R(6, 3)</code>, and <code class='latex inline'>S(8, - 1)</code>. What shape is this?</p>
<p>Find the length of <code class='latex inline'>QR</code>.</p><img src="/qimages/739" />
<p>The points A(5, -3), B(-2, 4), and C(-1, 7) are three vertices of a parallelogram ABCD. Find the coordinates of vertex D. Check your answer by using a different method.</p>
<p>Show that the intersection of the line segments joining the midpoints of the opposite sides of a square is the same point as the midpoints of the diagonals.</p>
<p>Verify that quadrilateral <code class='latex inline'>JKLM</code> is a kite.</p><img src="/qimages/742" />
<p>Which of the line segments inside each quadrilateral are equal in length?</p><img src="/qimages/736" /><img src="/qimages/737" />
<p>A trapezoid has vertices at <code class='latex inline'>A(1,2), B(-2,1), C(-4,-2),</code> and <code class='latex inline'>D(2,0)</code>.</p> <ul> <li>Show that the line segment joining the midpoints of <code class='latex inline'>BC</code> and <code class='latex inline'>AD</code> is parallel to both <code class='latex inline'>AB</code> and <code class='latex inline'>DC</code>.</li> </ul>
<p>The sides of quadrilateral ABCD have the following slopes.</p> <ul> <li>slope of AB: <code class='latex inline'>-5</code></li> <li>slope of BC: <code class='latex inline'>-\frac{1}{7}</code></li> <li>slope of CD: <code class='latex inline'>-5</code></li> <li>slope of AD: <code class='latex inline'>-\frac{1}{7}</code></li> </ul> <p>What types of quadrilateral could ABCD be? </p>
<p>What is the length of the diagonals of quadrilateral <code class='latex inline'>ABCD</code> at the right are equal in length.</p><img src="/qimages/717" />
<p>The golden ratio is <code class='latex inline'>\phi = \frac{1 + \sqrt{5}}{2}</code>. Show that <code class='latex inline'>\frac{1}{\phi} = \phi - 1</code>.</p>
<p>Verify that the diagonals of the rectangle with vertices <code class='latex inline'>J(-2, 1), K(2, 3), L(4, -1)</code>, and <code class='latex inline'>M(0, -3)</code> bisect each other at right angles.</p>
<p>Find the length of <code class='latex inline'>EG</code>.</p><img src="/qimages/738" />
<p>Which line segments are parallel in the figure below?</p><img src="/qimages/738" />
How did you do?
I failed
I think I failed
I think I got it
I got it
Another question?
Found an error or missing video? We'll update it within the hour! 👉
Report it
Save videos to My Cheatsheet for later, for easy studying.