Respuesta :
Given:
A(5, 1), B(5, 5), C(1, 3)
Q(-6, 5), R(-4, -5), S(__, __)
To find the coordinates of S that would prove that ABC is similar to QRS, we have:
First Find the distance betweem AB and the distance between QR using the distance formula below:
[tex]\begin{gathered} D=\sqrt[]{(x2-x1)^2+(y2-y1)^2} \\ \end{gathered}[/tex]Distance between AB:
[tex]\begin{gathered} AB=\sqrt[]{(5-5)^2+(5-1)^2} \\ \\ AB=\sqrt[]{0+16} \\ \\ AB\text{ = 4} \end{gathered}[/tex]Distance between QR:
[tex]\begin{gathered} QR=\sqrt[]{(-4--6)^2+(-5-}-5)^2 \\ \\ QR=\sqrt[]{(-4+6)^2+(-5+5)^2} \\ \\ QR\text{ = }\sqrt[]{(2)^2+(0)^2} \\ \\ QR=\sqrt[]{4} \\ \\ QR\text{ = 2} \end{gathered}[/tex]Since ABC is similar to QRS, we have:
AB ~ QR
AB = 4
QR = 2
The scale factor is:
[tex]\frac{AB}{QR}=\frac{4}{2}=2[/tex]Since the scale factor is 2, Let's find the coordinates of S:
Find the distance between BC and AC .
Thus, we have:
The coordinates of S that would prove that ABC is similar to QRS is:
(-3, -5)
Choice C is correct
ANSWER:
C. (-3 -5)
