points a, b, and, c have xy - coordinates ( 20 ), ( 812 ), and ( 140 ), respectively. points x, y, and z have xy - coordinates ( 60 ), ( 84 ), and ( 100 ), respectively. what fraction c of the area of triangle abc is the area of triangle xyz? Select
A) 1 / 9	B) 1 / 8	C) 1 / 6	D) 1 / 5	E) 1 / 3
<gadget id="calculator">4 * 4</gadget>
<output>16</output>

<gadget id="calculator">16 / 2</gadget>
<output>8</output>

<gadget id="calculator">4 * 2</gadget>
<output>8</output>

<gadget id="calculator">20 - 8</gadget>
<output>12</output>

<gadget id="calculator">12 / 2</gadget>
<output>6</output>

<gadget id="calculator">12 * 6</gadget>
<output>72</output>

<gadget id="calculator">8 / 72</gadget>
<output>1/9 = around 0.111111</output>

<result>A</result>
points a, b, and, c have xy - coordinates ( 20 ), ( 812 ), and ( 140 ), respectively. points x, y, and z have xy - coordinates ( 60 ), ( 84 ), and ( 100 ), respectively. what fraction c of the area of triangle abc is the area of triangle xyz?
divide(divide(multiply(const_4, const_4), const_2), multiply(subtract(20, multiply(const_4, const_2)), divide(subtract(20, multiply(const_4, const_2)), const_2)))
if you notice , both triangles abc and xyz have a side on x axis . we can take these sides as bases for each triangle , therefore area of abc is 1 / 2 * 12 * 12 ( height of abc is the y coordinate of the third point ( 812 ) ) similarly area of xyz is 1 / 2 * 4 * 4 dividing area of xyz with that of abc gives c = 1 / 9 . a