Question

Triangle EFG and triangle HJK are similar triangles.

Answer 1

Option B:

$\frac{1-(-1)}{2-0}=\frac{2-(-2)}{3-(-1)}$

Solution:

Triangle EFG and Triangle HJK are similar triangles.

Both triangles have the common line.

In triangle EFG, E(0, –1) and G(2, 1).

Here, $x_1=0, y_1=-1, x_2=2, y_2=1$

Slope of the line:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{1-(-1)}{2-0}$ – – – – (1)

$m=\frac{2}{2}$

m = 1

In triangle HJK, H(–1, –2) and K(3, 2).

Here, $x_1=-1, y_1=-2, x_2=3, y_2=2$

Slope of the line:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

$m=\frac{2-(-2)}{3-(-1)}$ – – – – (2)

$m=\frac{4}{4}$

m = 1

Both slopes are equal. so that (1) and (2) are equal.

$\frac{1-(-1)}{2-0}=\frac{2-(-2)}{3-(-1)}$

Hence Option B is the correct answer.