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:

`(3 - 7)/(-4 - (-7)) = (-5 - 3)/(2 - (-4))`

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 = (y_2 - y_1)/(x_2 - x_1)`

Where

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

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

`m = (y_2 - y_1)/(x_2 - x_1)` becomes

`m = (3 - 7)/(-4 - (-7))` --------- (1)

Next, we calculate the slope (m) of RST

Here, we consider R and T

`m = (y_2 - y_1)/(x_2 - x_1)`

Where

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

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

`m = (y_2 - y_1)/(x_2 - x_1)` becomes

`m = (-5 - 3)/(2 - (-4))` ---------- (2)

Next, we equate (1) and (2)

`(3 - 7)/(-4 - (-7)) = (-5 - 3)/(2 - (-4))`

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