Question

Find the midpoint of the line segment connecting the following line 1.(10,4) and (5,-6) 2.(6,3 and (9,-9) 3.(5,5) and (-2,-2) 4.(-1,3) and (4,4) 5.(5,2) and (3,6) 6.(0,4) and (4,0) 7.(5,0) and (7,-16)

Answer 1

Solution :-

Midpoint formula = $(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2})$

1. (10,4) and (5,-6)

Here,

$x_1 = 10\:\:\:\:\:x_2 = 5\\\\y_1 = 4\:\:\:\:\:y_2 = -6$

Midpoint of (10,4) and (5,-6)

$=(\dfrac{10+5}{2},\dfrac{4+(-6)}{2})\\\\=(\dfrac{15}{2},\dfrac{-2}{2})\\\\=(7.5,-1)$

2. (6,3) and (9,-9)

Here,

$x_1 = 6\:\:\:\:\:x_2 = 9\\\\y_1 = 3\:\:\:\:\:y_2 = -9$

Midpoint of (6,3) and (9,-9)

$=(\dfrac{6+9}{2},\dfrac{3+(-9)}{2})\\\\=(\dfrac{15}{2},\dfrac{-6}{2})\\\\=(7.5,-3)$

3. (5,5) and (-2,-2)

Here,

$x_1 = 5\:\:\:\:\:x_2 = -2\\\\y_1 = 5\:\:\:\:\:y_2 = -2$

Midpoint of (5,5) and (-2,-2)

$=(\dfrac{5+(-2)}{2},\dfrac{5+(-2)}{2})\\\\=(\dfrac{3}{2},\dfrac{3}{2})\\\\=(1.5,1.5)$

4. (-1,3) and (4,4)

Here,

$x_1 = -1\:\:\:\:\:x_2 = 4\\\\y_1 = 3\:\:\:\:\:y_2 = 4$

Midpoint of (-1,3) and (4,4)

$=(\dfrac{-1+4}{2},\dfrac{3+4}{2})\\\\=(\dfrac{3}{2},\dfrac{7}{2})\\\\=(1.5,3.5)$

5. (5,2) and (3,6)

Here,

$x_1 = 5\:\:\:\:\:x_2 = 3\\\\y_1 = 5\:\:\:\:\:y_2 = 6$

Midpoint of (5,2) and (3,6)

$=(\dfrac{5+3}{2},\dfrac{2+6}{2})\\\\=(\dfrac{8}{2},\dfrac{8}{2})\\\\=(4,4)$

5. (0,4) and (4,0)

Here,

$x_1 = 0\:\:\:\:\:x_2 = 4\\\\y_1 = 4\:\:\:\:\:y_2 = 0$

Midpoint of (5,2) and (3,6)

$=(\dfrac{0+4}{2},\dfrac{4+0)}{2})\\\\=(\dfrac{4}{2},\dfrac{4}{2})\\\\=(2,2)$

5. (5,0) and (7,-16)

Here,

$x_1 = 5\:\:\:\:\:x_2 = 7\\\\y_1 = 0\:\:\:\:\:y_2 = -16$

Midpoint of (5,0) and (7,-16)

$=(\dfrac{5+7}{2},\dfrac{0+(-16)}{2})\\\\=(\dfrac{12}{2},\dfrac{-16}{2})\\\\=(6,-8)$