Question

The line segment AB has the endpoints A(−1,−2) and B(1,6). Calculate: The midpoint of AB, The length of AB and The slope of the line passing through points A and B.

A) a) (0, 2), b) 4, c) -4
B) a) (0, 4), b) 5, c) -1
C) a) (0, 2), b) 10, c) -4
D) a) (1, 4), b) 7, c) 4

Answer 1

The midpoint of AB is (0,2), the length of AB is 10, and the slope of the line passing through A and B is 4.

Step-by-step explanation:

The midpoint of a line segment can be found by averaging the x-coordinates of the endpoints and averaging the y-coordinates of the endpoints. So for the line segment AB with endpoints A(-1,-2) and B(1,6), the midpoint is (0,2).

The length of a line segment can be found using the distance formula, which calculates the distance between two points. The formula is √((x2-x1)²+(y2-y1)²). So for AB, the length is √((1-(-1))²+(6-(-2))²) = √(2²+8²) = 10.

The slope of a line can be found using the formula (y2-y1)/(x2-x1). So for AB, the slope is (6-(-2))/(1-(-1)) = 8/2 = 4.