Question

The points A(−5, 4), B(−1, −2) and C(5, 2) are the vertices of an isosceles right-angled triangle where the right angle is at B. Find the coordinates of D so that ABCD is a square

Answer 1

Since ABCD is a square

Mid-point of AC = mid-point of BD

Let the point D be (a, b)

Mid−point of a line = `((x_1 + x_2)/2, (y_1 + y_2)/2)`

Mid−point of AC = `((5 - 5)/2, 2 + 4/2)`

`(0/2, 6/2)` = (0, 3)

Mid−point of BD = `((-1 + "a")/2, (-2 + "b")/2)`

But mid-point of BD = Mid-point of AC

`((-1 + "a")/2, (-2 + "b")/2)` = (0, 3)

`(-1 + "a")/2` = 0

−1 + a = 0

a = 1

`((-2 + b)/2)`

−2 + b = 6

b = 6 + 2 = 8

∴ The vertices D is (1, 8).