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

Answer:

The slope of the line is: $\frac{-1}{6}$

The midpoint is located in (1, 8.5)

The distance between the points is 2.236

Step-by-step explanation:

The slope of the line can be calculated by:

$m = \frac{y_2 - y_1}{x_2 - x_1} = \frac{8-9}{4+2} = \frac{-1}{6}$

The midpoint can be calculated by:

$midpoint = (\frac{x_1 + x_2}{2}, \frac{y_1 + y_2}{2})\\midpoint = (\frac{-2 + 4}{2}, \frac{9 + 8}{2})\\midpoint = (1, 8.5)$

The distance between two points is:

$distance = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\\distance = \sqrt{(-4+2)^2 + (8 - 9)^2}\\distance = \sqrt{(-2)^2 + (-1)^2}\\distance = \sqrt{4 + 1} = \sqrt{5} = 2.236$