# If the points A (

Formula used:

Let A, B, C and D represent the points (6, 1), (8, 2), (9, 4) and (p, 3)

Distance of AB

AB = √ ((8 – 6))2 + (2 – 1)2)

AB = √ ((2)2 + (1)2)

AB = √ (4 + 1)

AB = √ 5

Distance of CD

CD = √ ((p – 9)2 + (3 – 4)2)

CD = √ ((p – 9)2 + (1)2)

CD = √ (p2 + 81 – 18p + 1)

CD = √ p2 – 18p + 82

i.e., The opposite sides are equal.

AB = CD

√5 = √ p2 – 18p + 82

Squaring both sides

5 = p2 – 18p + 82

p2 – 18p + 82 – 5 =0

p2 – 18p + 77 = 0

p2 – 11p – 7p + 77 = 0

p(p – 11) – 7(p – 11)= 0

(p – 11)(p – 7) = 0

p – 11 = 0 or p – 7 = 0

p = 11 or p = 7

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