NDA 2 2024 Maths, question 63

Topic: Analytical geometry

Passage · Q63 to Q64

$ABCD$ is an isosceles trapezium and $AB$ is parallel to $DC$ . Let $A(2,3)$ , $B(4,3)$ , $C(5,1)$ be the vertices.

Q63

What are the coordinates of vertex $D$ ?

(a) $(2,1)$
(b) $(1,2)$
(c) $(1,1)$ Correct answer
(d) $(3,1)$

Solution.

Answer: (c) $(1,1)$

The parallel base DC is horizontal through C, so D=(d,1).
Equal legs give (d−2)²+4=(5−4)²+4, hence d=1 or 3.
The isosceles trapezium with only one pair of parallel sides uses d=1; d=3 would form a parallelogram.
Thus D=(1,1), matching the usual trapezium convention.