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Find $x$ if triangle ABC with A(1, 0), B(5, 0) and C $(x$ , 2) has a right angle at C.

Class 10Classifying Shapes by CoordinatesGeometry — Coordinates

A3
B5
C4
D2

Step-by-Step Solution

Right angle at

C

means

A C^{2} + B C^{2} = A B^{2} : (x - 1)^{2} + 4 + (x - 5)^{2} + 4 = 16

gives

2 x^{2} - 12 x + 18 = 0

, i.e.

(x - 3)^{2} = 0

, so

x = 3

.

Answer: A) 3

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