Question

Two points A (-2, 9) and B (4, 8) lie on a line l. (i) Find the slope of the line l. (ii) Find the coordinates of the midpoint of the points A and B (iii) Find the distance between points A and B.

Answer 1

`m=-(1)/(6) \approx -0.1667`

`M=(1,(17)/(2) )=(1,8.5)`

`d=√(37) \approx 6.083`

Explanation:

(i) For two different points on a line, the slope m is defined as the difference on the y-axis divided by the difference on the x-axis:

`m=(\Delta y)/(\Delta x) =(y_2-y_1)/(x_2-x_1)`

Where:

`(x_1,y_1)=(-2,9)\\\\(x_2 , y_2)=(4,8)`

So:

`m=(8-9)/(4-(-2)) =(-1)/(6) \approx -0.1667`

(ii)

To find the coordinates of the midpoint, you can use the following formula:

`M=((x_1+x_2)/(2) , (y_1+y_2)/(2) )`

Therefore:

`M=((-2+4)/(2) , (9+8)/(2) )=((2)/(2) , (17)/(2) ) =(1,8.5 )`

(iii) The distance between two points is given by the following formula:

`d=\sqrt{(x_2-x_1)^(2)+(y_2-y_1)^(2) }`

Hence:

`d=\sqrt{(4-(-2))^(2)+(8-9)^(2) } =\sqrt{(6)^(2)+(-1)^(2) } =√(36+1) =√(37) \\\\d\approx 6.083`