Question

if p(4,k) is q(k,5) r(2,k) and s(k,5) are the coordnates of rectangle,find the value of k ,also find coordnates.




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Answer 1

Explanation:

since opposite side of rectangle are congruent .

d(P,Q) = d(R,S)

√[(k- 4)^2 + (5-k)^2] = √[(k-2)^2 + (5- k)^2]

Squaring on both the sides of the equation...

(k-4)^2 + (5-k)^2 = (k-2)^2 + (5-k)^2

cancelling (5-k)^2 on both the sides....

k^2 - 8k + 16 = k^2 - 4k + 4

cancelling k^2 on both the sides and dividing the whole equation by 4...

-2k + 4 = - k + 1

- k + 2k = 4-1

k = 3.

therefore the the coordinates of the rectangle are

P(4,3) ; Q(3,5) ; R(2,3) and S(3,5).