15. Q15
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<p>A design plan for a thin triangular computer component shows the vertices at points <code class='latex inline'>(8, 12), (l2,4)</code> and <code class='latex inline'>(2,8)</code>. Determine the coordinates of the centre of mass.</p>
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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
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<p>A stained glass window is in the shape of a triangle, with vertices at <code class='latex inline'>A(-1,-2), B(-2,1), </code> and <code class='latex inline'>C(5,0)</code>. <code class='latex inline'>\triangle XYZ</code> is formed inside <code class='latex inline'>\triangle ABC</code> by joining the midpoints of the three sides. The glass that is used for <code class='latex inline'>\triangle XYZ</code> is blue, but the remainder of <code class='latex inline'>\triangle ABC</code> is green. Determine the ratio of green to blue glass used.</p>
<p> <code class='latex inline'>\triangle OBC</code> with vertices <code class='latex inline'>O(0, 0), B(6, 0)</code>, and <code class='latex inline'>C(0, 9)</code> in the coordinate system. Find the coordinates of the centroid of the triangle.</p>
<p><code class='latex inline'>\triangle PQR</code> has vertices at <code class='latex inline'>P(-12,6), Q(4,0),</code> and <code class='latex inline'>R(-8,-6)</code>. Use analytic geometry to determine the coordinates of the centroid (the point where the medians intersect).</p>
<p>A design plan for a thin triangular computer component shows the vertices at points <code class='latex inline'>(8, 12), (l2,4)</code> and <code class='latex inline'>(2,8)</code>. Determine the coordinates of the centre of mass.</p>
<p>A landscape architect is drawing plans for a rigid triangular canopy to provide shade in a courtyard. On the drawing, the vertices of the canopy are <code class='latex inline'>0(0, 0), P(10, 0)</code>, and <code class='latex inline'>Q(2, 12)</code>. </p><p>A single pole will support the canopy.</p><p><strong>(a)</strong> Verify that the triangular canopy has a centroid.</p><p><strong>(b)</strong> Explain why the centroid is a good location for attaching the canopy to the support pole.</p>
<p>A triangle has vertices at <code class='latex inline'>P(-1,2), Q(4,-4), </code> and <code class='latex inline'>R(1,2)</code>. Show that the centroid divides each median in the ratio <code class='latex inline'>2:1</code> by finding the length of</p><p>a) <code class='latex inline'>\overline{MG}</code></p><p>b) <code class='latex inline'>\overline{GQ}</code></p><p>where <code class='latex inline'>G</code> is the location of the centroid.</p>
<p><code class='latex inline'>A(3, 4), B(-2, 0)</code>, and <code class='latex inline'>C(5, 0)</code>. <code class='latex inline'>D, E</code>, and <code class='latex inline'>F</code> are the midpoints of each side.</p> <ul> <li>How is the ratio of the lengths of corresponding sides related to the ratio of the areas of <code class='latex inline'>\triangle ABC</code> and <code class='latex inline'>\triangle DEF</code>?</li> </ul>
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