Question

Find the coordinates of the point equidistant from the points A(1,2), B(3,-4) and
C(5,-6) is
a) (2,3), b) (-1,-2) c) (0,3) d) (1,3).​

Answer 1

Answer:x^2 + 1– 2x + y^2 + 4 – 4y = x^2 + 9 -6x + y^2 + 16 + 8y = x 2 + 25– 10x + y^2 + 36 + 12y

⇒ – 2x– 4y + 5 = -6x + 8y +25= – 10x + 12y+61

– 2x– 4y + 5 = -6x + 8y +25

⇒ – 2x– 4y + 5 +6x – 8y -25=0

⇒ 4x– 12y -20=0

⇒ x– 3y – 5 =0….(i)

– 2x– 4y + 5 = – 10x + 12y+61

⇒- 2x– 4y + 5 +10x – 12y-61=0

⇒8x– 16y -56=0

⇒x– 2y -7=0….(ii)

Solving (i) and (ii)

x = 11, y = 2

Thus, the required point is (11, 2)