Mathematics · Coordinate Geometry · NCERT Examples

Example 10

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Mathematics · Chapter 7 · NCERT Examples

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NCERT Example

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.

Board-exam working:

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

Midpoint of AC:

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

Midpoint of BD:

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

Equating the x-coordinates:

\frac{15}{2}=\frac{8+p}{2}

15=8+p

p=7

p = 7.

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