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:

Option D is correct.

Step-by-step explanation:

By looking at the graph attached, first look up the coordinates of the points A, C, D and G in order to find their required slopes.

Now, finding the coordinates of the points from the graph :

Coordinates of A = (-7,4)

Coordinates of C = (-4,10)

Coordinates of D = (-10,8)

Coordinates of G = (-1,-4)

Now, slope (m) between two points is given by :

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

$\text{Slope of AC, }m_1=\frac{0-4}{-4-(-7)}\\\\\text{And, Slope of DG, }m_2=\frac{-4-8}{-1-(-10)}\\\\\text{Now, putting }m_1=m_2\\\\ \implies \frac{0-4}{-4-(-7)}=\frac{-4-8}{-1-(-10)}$

Hence, Option D is correct.

Answer 2

Answer:

Option D is correct.

Slope of AC = Slope of DG

$\frac{0-4}{-4-(-7)}=\frac{-4-8}{-1-(-10)}$

Step-by-step explanation:

Similar triangle states that if two triangles are similar then, their corresponding sides are in proportion.

As per the statement:

Triangle ABC and triangle DEG are similar right triangles.

By definition:

Corresponding sides are in proportion then;

$\frac{AB}{DE}=\frac{BC}{EG}=\frac{AC}{DG}$

From the graph:

The coordinate of A and C are:

A (-7, 4) and C(-4, 0)

Formula for slope is given by:

$\text{Slope} =\frac{y_2-y_1}{x_2-x_1}$

then;

$\text{Slope of AC} =\frac{0-4}{-4-(-7)}$

The coordinates of D and G are:

D(-10, 8) and G(-1, -4)

then;

$\text{Slope of DG} =\frac{-4-8}{-1-(-10)}$

Slope of AC = Slope of DG

$\frac{0-4}{-4-(-7)}=\frac{-4-8}{-1-(-10)}$