Question

Triangle ABC and triangle DEG are similar right triangles. Which proportion can be used to show that the slope of AC is equal to the slope of DG?





A)


4 − (−7) / 0 − 4 = −1 − 10 / 4 − 8




B)


−4 − (−7) / 0 − 4= 4 − 8 / −1 − (−10)




C)


0 − 4 / −4 − (−7) = −1 − (−10) / −4 − 8




D)


0 − 4 / −4 − (−7) = −4 − 8 / −1 − (−10)

Answer 1

ANSWER

$D) \: \: \frac{0 - 4}{ - 4 - ( - 7)}=\frac{ - 4 - 8}{ - 1 - ( - 7)}$



EXPLANATION


The slope can be calculated using the formula,

$m=\frac{y_2-y_1}{x_2-x_1}$

Using A(-7,4) and C(-4,0), the slope of AC is


$= \frac{0 - 4}{ - 4 - ( - 7)}$



Using D(-10,8) and G(-1,-4), the slope of DG is




$= \frac{ - 4 - 8}{ - 1 - ( - 7)}$


Therefore the required proportion is,



$\frac{0 - 4}{ - 4 - ( - 7)}=\frac{ - 4 - 8}{ - 1 - ( - 7)}$