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 passing through the points (-2, 9) and (4, 8) is -1/6. The midpoint of these points is (1, 8.5). The distance between the points is approximately 6.08.

Step-by-step explanation:

To find the slope of a line passing through two points, we can use the formula:
Slope (m) = (y2 - y1) / (x2 - x1)

Given the two points A (-2, 9) and B (4, 8), we can substitute the values into the formula:
Slope (m) = (8 - 9) / (4 - (-2))
Slope (m) = -1 / 6

To find the midpoint of the two points, we can use the formula:
Midpoint (x, y) = ((x1 + x2) / 2, (y1 + y2) / 2)

Substituting the values of the two points A (-2, 9) and B (4, 8) into the formula, we get:
Midpoint (x, y) = ((-2 + 4) / 2, (9 + 8) / 2)
Midpoint (x, y) = (1, 8.5)

To find the distance between the two points, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the values of the two points A (-2, 9) and B (4, 8) into the formula, we get:
Distance = sqrt((4 - (-2))^2 + (8 - 9)^2)
Distance = sqrt(36 + 1)
Distance = sqrt(37) or approximately 6.08