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For which value of k is C(k, 4) equidistant from A(2, 1) and B(6, 1), making triangle ABC isosceles with CA = CB?

Class 10Classifying Shapes by CoordinatesGeometry — Coordinates

A4
B6
C2
D3

Step-by-Step Solution

C A^{2} = (k - 2)^{2} + 9, C B^{2} = (k - 6)^{2} + 9

. Equal when

(k - 2)^{2} = (k - 6)^{2} \Rightarrow - 4 k + 4 = - 12 k + 36 \Rightarrow k = 4. C

sits right above the midpoint (4, 1) of

A B

.

Answer: A) 4

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