8. Q8
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Similar Question 1
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /> <ul> <li>Determine the slope of AD.</li> <li>Determine the equation of the line that contains AD.</li> </ul>
Similar Question 2
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /><p>Determine the area of <code class='latex inline'>\triangle ABC</code>.</p>
Similar Question 3
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /><p>Determine the area of <code class='latex inline'>\triangle ABC</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><code class='latex inline'>\triangle LMN</code> has vertices at <code class='latex inline'>L(3,4), M(4,-3),</code> and <code class='latex inline'>N(-4,-1)</code>. Use analytic geometry to determine the area of the triangle.</p>
<p>A cable company is connecting a new customer to its cable network. On a site plan, the customer&#39;s house has coordinates <code class='latex inline'>H(7, 17)</code>. The equation <code class='latex inline'>y = \frac{1}{2}x + 4</code> represents the existing trunk cable. The cable company wants to keep the branch to the customer&#39;s house as short as possible.</p> <ul> <li>Where should the cable company make the connection to the trunk cable?</li> </ul>
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /> <ul> <li>Determine the slope of AD.</li> <li>Determine the equation of the line that contains AD.</li> </ul>
<p>A triangle has vertices at <code class='latex inline'>A(-3,2), B(-5,-6),</code> and <code class='latex inline'>C(5,0)</code>.</p> <ul> <li><p>i. Determine the equation of the altitude from vertex <code class='latex inline'>A</code>.</p></li> <li><p>ii. Determine the equation of the perpendicular bisector of <code class='latex inline'>BC</code>.</p></li> <li><p>iii. What type of triangle is <code class='latex inline'>\triangle ABC</code>? Explain how you know.</p></li> </ul>
<p>a) Draw the triangle with vertices <code class='latex inline'>D(5, 25), E(210,1)</code>, and <code class='latex inline'>F(3, 210)</code>.</p><p>b) Use analytic geometry to Classify <code class='latex inline'>\triangle DEF</code>.</p><p>c) Determine the area of <code class='latex inline'>\triangle DEF</code>.</p>
<p>A triangle has vertices <code class='latex inline'>J(-2, 0), K(4, -3)</code>, and <code class='latex inline'>L(8, 8)</code>.</p> <ul> <li>Find the area of <code class='latex inline'>\triangle JKL</code>.</li> </ul>
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /><p>Determine the equation of the line that contains <code class='latex inline'>BC</code>.</p>
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /><p>Determine the coordinates of point <code class='latex inline'>D</code>.</p>
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /><p><strong>a)</strong> Determine the slope of <code class='latex inline'>BC</code>.</p><p><strong>b)</strong> Determine the slope of <code class='latex inline'>AD</code>.</p><p><strong>c)</strong> Determine the equation of the line that contain <code class='latex inline'>AD</code>.</p>
<p>Dylan and Indira are hiking on the Caledon Hills section of the Bruce Trail. They have reached the point that has coordinates <code class='latex inline'>(6, 8)</code> on their map of the trail. They want to hike out to the straight section of Hockley Road that joins points <code class='latex inline'>(4, 7)</code> and <code class='latex inline'>(6, 5)</code>.</p><p>a) At what point will they reach Hockley Road if they take the shortest possible route?</p><p>b) Explain why the shortest route might not be the best route.</p>
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /><p>Determine the lengths of <code class='latex inline'>BC</code> and <code class='latex inline'>AD</code>.</p>
<p>A utility company is running new power lines to two cottages. On a site plan, the cottages have coordinates <code class='latex inline'>A(6, 7)</code> and <code class='latex inline'>B(13, 6)</code> and the closest transformer is at <code class='latex inline'>T(13, 14)</code>. </p><p>The utility will run a line straight from the transformer to one of the cottages and then connect the other cottage to that line using the shortest possible route.</p><p>a) Draw a diagram on a grid to show the two possible ways to run the power lines.</p><p>b) Determine which route will require the least cable.</p>
<p><code class='latex inline'>\triangle ABC</code> has vertices at <code class='latex inline'>A(-1,4), B(-1,-2), </code> and <code class='latex inline'>C(5,1)</code>. The altitude from vertex <code class='latex inline'>A</code> meets <code class='latex inline'>BC</code> at point <code class='latex inline'>D</code>.</p><img src="/qimages/720" /><p>Determine the area of <code class='latex inline'>\triangle ABC</code>.</p>
<p>A map shows a main gas pipeline running straight from <code class='latex inline'>A(45, 60)</code> to <code class='latex inline'>B(65, 40)</code>.</p><p>a) How long is the section of pipeline from A to B if each unit on the map grid represents 1 km?</p><p>b) A branch pipeline runs perpendicular to the main pipeline and meets it at a point halfway between A and B. Find the coordinates of this point.</p><p>c) Is the point <code class='latex inline'>C(63, 54)</code> on the branch pipeline? Explain your reasoning.</p><p>d) What is the shortest route for connecting point C to the main pipeline? Explain.</p>
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