Answer: x = 12.5
Step-by-step explanation:
P = (2, 5)
Q = (x, -3)
R = (7, 9)
[tex]d_{PQ}=d_{QR}[/tex]
[tex]d_{PQ}=\sqrt{(2-x)^2+(5+3)^2}, \quad d_{QR} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex]\sqrt{(2-x)^2+(5+3)^2} = \sqrt{(x-7)^2+(-3-9)^2}[/tex]
[tex](2-x)^2+(5+3)^2 = (x-7)^2+(-3-9)^2[/tex]
[tex]4-4x+x^2+64 = x^2-14x+49+144[/tex]
[tex]4x+68 = -14x+193[/tex]
[tex]10x+68 = 193[/tex]
[tex]10x= 125[/tex]
x = 12.5
