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A(0, 0) and B(4, 0) are two vertices of an equilateral triangle whose third vertex C is in the first quadrant. Find C.

Class 10Classifying Shapes by CoordinatesGeometry — Coordinates

A(2, 4)
B $(2, 23)$
C $(4, 23)$
D $(2, 3)$

Step-by-Step Solution

C

lies above the midpoint (2, 0) of AB, so

C

= (2, h). AC = 4 gives

4 + h^{2} = 16, h = 23

. Check BC =

4 + 12 = 4

.

Answer: B)

(2, 23)

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