Question

Two points A (-2, 9) and B (4,8) lie on a line /.

(i)Find the slope of the line /

(ii)Find the coordinates of the midpoint of the points A and B
or up

(iii) Find the distance between points A and B.​

Answer 1

Answer:

Step-by-step explanation:

1. Slope = (8 - 9)/(4 - (-2)) = -1/6

2. midpoint coordinates = ((-2 + 4)/2, (8 + 9)/2) = (1, 17/2)

3. distance AB = $\sqrt{(4 - (-2))^{2} + (8 - 9)^{2}} = \sqrt{37} = 6.083 units$

Answer 2

Given:

Points: A (-2, 9) and B (4,8)

To find:

Slope=?

coordinates of the midpoint=?

distance between points A and B=?

Solution:

Formula:

$\ slope (M)= \frac{y_2-y_1}{x_2-x_1}\\\\\ midpoint = \frac{x_1+x_2}{2} ,\frac{y_1+y_2}{2} \\\\\ distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$

$x_1=-2\\y_1=9\\x_2=4\\y_2=8\\\to (M)= \frac{8-9}{4-(-2)}\\\\\to (M)= \frac{8-9}{4+2}\\\\\to (M)= \frac{-1}{6}$

$\to midpoint= \frac{-2+4}{2}, \frac{9+8}{2}\\\\\to midpoint= \frac{2}{2}, \frac{17}{2}\\\\\to midpoint= 1, \frac{17}{2}$

$\to distance =\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\\\\to distance =\sqrt{(4-(-2))^2+(8-9)^2}\\\\\to distance =\sqrt{(4+2)^2+(8-9)^2}\\\\\to distance =\sqrt{(6)^2+(-1)^2}\\\\\to distance =\sqrt{36+1}\\\\\to distance =\sqrt{37}$

$\bold{ M\ = -\frac{1}{6}}\\\\\bold{Midpoint = 1 ,\frac{17}{2}}\\\\\bold{Distance= \sqrt{37}}$