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)}

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MrRoyal MrRoyal · Answer 1 · 2020-11-23T07:14:59+01:00

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:

[tex]\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}[/tex]

Step-by-step explanation:

See attachment for complete question

From the attachment, we have that:

[tex]P = (-7,7)[/tex]

[tex]Q = (-7,3)[/tex]

[tex]R = (-4,3)[/tex]

[tex]S = (-4,5)[/tex]

[tex]T = (2,-5)[/tex]

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

Here, we consider P and R

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex]P(x_1,y_1) = (-7,7)[/tex]

[tex]R(x_2,y_2) = (-4,3)[/tex]

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes

[tex]m = \frac{3 - 7}{-4 - (-7)}[/tex] --------- (1)

Next, we calculate the slope (m) of RST

Here, we consider R and T

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex]

Where

[tex]R(x_1,y_1) = (-4,3)[/tex]

[tex]T (x_2,y_2)= (2,-5)[/tex]

[tex]m = \frac{y_2 - y_1}{x_2 - x_1}[/tex] becomes

[tex]m = \frac{-5 - 3}{2 - (-4)}[/tex] ---------- (2)

Next, we equate (1) and (2)

[tex]\frac{3 - 7}{-4 - (-7)} = \frac{-5 - 3}{2 - (-4)}[/tex]

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