CBSE 10th Math Sample Paper 2019 | Q16A

Section C | Diagonals of Parallelogram | Coordinate Geometry

This 2019 CBSE class 10 Maths 3 mark question is from Coordinate Geometry. Concept: diagonals of a parallelogram bisect each other and midpoint formula.

Question 16A: The points A(1, -2) , B(2, 3), C(k, 2) and D(-4, -3) are the vertices of a parallelogram. Find the value of k.

NCERT Solution to Class 10 Maths

Explanatory Answer | CBSE Sample Paper 2019 Q16 Internal Choice 1

Property: Diagonals of a parallelogram bisect each other.

∴ In a parallelogram ABCD, where AC and BD are the two diagonals, Midpoint of AC = Midpoint of BD
($$frac{\text{1 + k }}{\text{2}}$, $\frac{\text{−2 + 2 }}{\text{2}}$ ) =$$\frac{\text{−4 + 2}}{\text{2}}$ , $\frac{\text{−3 + 3}}{\text{2}}$ )
1 + $\frac{\text{k}}{\text{2}}$ = $\frac{−2}{2}$
1 + k = -2
k = -3

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