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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
Solution
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).
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