Question

Two vertices of a triangle are (4,-3) and (-2,5) if the circumcentre of the triangle is at (1,2) then the third vertex is

• A. (1,4)
• B. (3,4)
• C. (6,3)
• D. none of these

Answer 1

Answer: (A)

(1,4)

The vertices are $(4,-3),(-2,5)$

The circumcenter is $(1,2)$

The circumcenter is given as

$x_c=\frac{x_1+x_2+x_3}{3}1=\frac{4-2+x_3}{3}{x}_3=3-2=1$

&

$y_c=\frac{y_1+y_2+y_3}{3}2=\frac{-3+5+y_3}{3}{y}_3=6-2=4$

So the third vertex is $(1,4)$