NDA 2 2024 Maths, question 64

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.

Q64

What is the point of intersection of the diagonals of the trapezium?

(a) $(3,7/2)$
(b) $(3,7/3)$ Correct answer
(c) $(7/2,2)$
(d) $(5/2,2)$

Solution.

Answer: (b) $(3,7/3)$

Using D=(1,1), diagonal AC has equation y=3−(2/3)(x−2).
Symmetry puts the diagonal intersection on x=3, giving y=7/3.
Substituting (3,7/3) into BD verifies the point.