Question

Find the equation of the perpendicular bisector given the two endpoints of a line segment: (-2, -2) and (-1, 2).

A) y=−x

B) y=2x+2

C) y=−1/2x+3/2

D) y=1/x−1

Answer 1

To find the equation of the perpendicular bisector given two endpoints of a line segment, we can use the midpoint formula and the negative reciprocal of the slope of the line segment.

Step-by-step explanation:

To find the equation of the perpendicular bisector given two endpoints of a line segment, we can use the midpoint formula and the negative reciprocal of the slope of the line segment.

Step 1: Find the midpoint of the line segment using the coordinates of the endpoints. The midpoint formula is: x = (x1 + x2)/2 and y = (y1 + y2)/2. In this case, the midpoint is (-1.5,0).

Step 2: Calculate the slope of the line segment using the slope formula: m = (y2 - y1)/(x2 - x1). In this case, the slope is -4.

Step 3: Find the negative reciprocal of the slope to get the slope of the perpendicular bisector. In this case, the negative reciprocal is 1/4.

Step 4: Use the slope-intercept form of a line, y = mx + b, with the slope of the perpendicular bisector and the coordinates of the midpoint to find the equation. Plugging in the values, we get y = (1/4)x + 1/2.