Problems using mid-point formula — lesson. Mathematics State Board, Class 9.

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Problem

$1$ :

Find the mid-point of the vertices $A(1$ , $1)$ and $B(-1$ , $-1)$ .

Given:

The end points of the line segment are

$A(1$ ,

$1)$ and

$B(-1$ ,

$-1)$ .

$x_1 = 1$

$x_2 = -1$

$y_1 = 1$

$y_2 = -1$

Let

$M$ be the mid-point of the line segment.

$\text{Midpoint} = (\frac{x_1+x_2}{2}$ ,

$\frac{y_1+y_2}{2})$

$= (\frac{1 - 1}{2}$ ,

$\frac{1 - 1}{2})$

$= (\frac{0}{2}$ ,

$\frac{0}{2})$

$M = (0$ ,

$0)$

Problem

$2$ :

Find the mid-point of the vertices $A(9$ , $2)$ and $B(4$ , $5)$ .

Given:

The end points of the line segment are

$A(9$ ,

$2)$ and

$B(4$ ,

$3)$ .

$x_1 = 9$

$x_2 = 4$

$y_1 = 2$

$y_2 = 3$

Let

$M$ be the mid-point of the line segment.

$\text{Midpoint} = (\frac{x_1 + x_2}{2}$ ,

$\frac{y_1 + y_2}{2})$

$= (\frac{9 + 4}{2}$ ,

$\frac{2 + 3}{2})$

$M = (\frac{13}{2}$ ,

$\frac{5}{2})$

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4. Problems using mid-point formula

Theory: