Answer:
The coordinates of point B are: (29,-15)
Option D is correct option.
Step-by-step explanation:
Endpoint of diameter of a circle = A(5,7)
Centre of circle = P(17,-4)
We need to find coordinates of other endpoint of diameter of a circle i.e. B
The formula used is: [tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})[/tex]
We are given coordinates of centre (midpoint) P(17,-4)
and A (5,7) x₁=5, y₁=7
We need to find Point B i.e. (x₂,y₂)
Putting values and finding point B
[tex]Midpoint=(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2})\\(17,-4)=(\frac{5+x_2}{2}, \frac{7+y_2}{2})\\We\:can\:write:\\17=\frac{5+x_2}{2}\:and\: -4=\frac{7+y_2}{2}\\17\times 2=5+x_2\:and\: -4\times 2=7+y_2\\34=5+x_2\:and\: -8=7+y_2\\34-5=x_2\:and\: -8-7=y_2\\x_2=29\:and\: y_2=-15[/tex]
so, we get: x₂ = 29 ,y₂ = -15
The coordinates of point B are: (29,-15)
Option D is correct option.
