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For what positive value of k is the triangle with vertices A(0, 0), B(6, 0) and C(3, k) equilateral?

Class 10Classifying Shapes by CoordinatesGeometry — Coordinates

A $33$
B6
C3
D $63$

Step-by-Step Solution

Need AC = AB = 6:

9 + k^{2} = 6 \Rightarrow k^{2} = 27 \Rightarrow k = 33

. Then BC =

9 + 27 = 6

as well.

k = 6

would make AC =

45

.

Answer: A)

33

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