we are given that
both sides are equal
so, their length must be equal
[tex] HK=\sqrt{(p-1)^2+(5-2)^2} [/tex]
[tex] HK=\sqrt{(p-1)^2+9} [/tex]
now, we can find other side
[tex] JK=\sqrt{(p-7)^2+(5-2)^2} [/tex]
[tex] JK=\sqrt{(p-7)^2+9} [/tex]
now, we can set them equal
[tex] HK=JK [/tex]
[tex] \sqrt{(p-1)^2+9}=\sqrt{(p-7)^2+9} [/tex]
now, we can take square both sides
[tex] (p-1)^2+9=(p-7)^2+9 [/tex]
now, we can solve for p
[tex] (p-1)^2=(p-7)^2 [/tex]
[tex] p^2-2p+1=p^2-14p+49 [/tex]
[tex] -2p+1=-14p+49 [/tex]
[tex] 12p=48 [/tex]
[tex] p=4 [/tex]..............Answer
