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

The slope of the line is:
`(-1)/(6)`

The midpoint is located in (1, 8.5)

The distance between the points is 2.236

Explanation:

The slope of the line can be calculated by:

`m = (y_2 - y_1)/(x_2 - x_1) = (8-9)/(4+2) = (-1)/(6)`

The midpoint can be calculated by:

`midpoint = ((x_1 + x_2)/(2), (y_1 + y_2)/(2))\\midpoint = ((-2 + 4)/(2), (9 + 8)/(2))\\midpoint = (1, 8.5)`

The distance between two points is:

`distance = √((x_2 - x_1)^2 + (y_2 - y_1)^2)\\distance = √((-4+2)^2 + (8 - 9)^2)\\distance = √((-2)^2 + (-1)^2)\\distance = √(4 + 1) = √(5) = 2.236`