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Mathematics · Coordinate Geometry · NCERT Examples

Example 10

A complete, independently verified solution for NCERT Example 10.

Mathematics · Chapter 7 · NCERT Examples

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NCERT Example

Example 10

midpoint formula · parallelogram · diagonals

If A(6, 1), B(8, 2), C(9, 4) and D(p, 3) are the vertices of a parallelogram in order, find p.

Solution

Board-exam working:

The diagonals of a parallelogram bisect each other. Therefore, the midpoint of AC equals the midpoint of BD.

Midpoint of AC:

(6+92,1+42)=(152,52)\left(\frac{6+9}{2},\frac{1+4}{2}\right)=\left(\frac{15}{2},\frac52\right)

Midpoint of BD:

(8+p2,2+32)=(8+p2,52)\left(\frac{8+p}{2},\frac{2+3}{2}\right)=\left(\frac{8+p}{2},\frac52\right)

Equating the x-coordinates:

152=8+p2\frac{15}{2}=\frac{8+p}{2}
15=8+p15=8+p
p=7p=7

Final answer

p = 7.