Question

Triangles PQR and RST are similar right triangles. ​ ​​Which proportion can be used to show that the slope of LaTeX: \overline{PR}P R ¯ is equal to the slope of LaTeX: \overline{RT}R T ¯? Group of answer choices LaTeX: \frac{-4-\left(-3\right)}{-7-7}=\frac{2-\left(-5\right)}{-4-3}− 4 − ( − 3 ) − 7 − 7 = 2 − ( − 5 ) − 4 − 3 LaTeX: \frac{3-7}{-4-\left(-7\right)}=\frac{-5-3}{2-\left(-4\right)}3 − 7 − 4 − ( − 7 ) = − 5 − 3 2 − ( − 4 ) LaTeX: \frac{-4-\left(-7\right)}{3-7}=\frac{2-\left(-4\right)}{-5-3}− 4 − ( − 7 ) 3 − 7 = 2 − ( − 4 ) − 5 − 3 LaTeX: \frac{3-\left(-4\right)}{7-\left(-7\right)}=\frac{-5-2}{3-\left(-4\right)}

Answer 1

Question:

Triangles PQR and RST are similar right triangles.  Which proportion can be used to show that the slope of PR is equal to the slope of RT?

Answer:

$\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}$

Step-by-step explanation:

See attachment for complete question

From the attachment, we have that:

$P = (-7,7)$

$Q = (-7,3)$

$R = (-4,3)$

$S = (-4,5)$

$T = (2,-5)$

First, we need to calculate the slope (m) of PQR

Here, we consider P and R

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

Where

$P(x_1,y_1) = (-7,7)$

$R(x_2,y_2) = (-4,3)$

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

$m = \frac{3 - 7}{-4 - (-7)}$ --------- (1)

Next, we calculate the slope (m) of RST

Here, we consider R and T

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

Where

$R(x_1,y_1) = (-4,3)$

$T (x_2,y_2)= (2,-5)$

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

$m = \frac{-5 - 3}{2 - (-4)}$ ---------- (2)

Next, we equate (1) and (2)

$\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}$

From the list of given options (see attachment), option A answers the question