171k views
2 votes
The midpoint of the line segment joining P(-2, 3) and Q(4,-1) is M.

The point C has coordinates (-1,-2).
Show that CM is perpendicular to PQ.​

2 Answers

4 votes

Final answer:

The midpoint M of PQ is defined by averaging the coordinates of P and Q. The slopes of CM and PQ are then found and shown to be negative reciprocals, proving CM is perpendicular to PQ.

Step-by-step explanation:

To show that CM is perpendicular to PQ, we first need to find the coordinates of the midpoint M of the line segment PQ. The midpoint M of a segment with endpoints P(-2, 3) and Q(4, -1) is found by averaging the x and y coordinates of P and Q, which gives us M(1, 1). Next, we determine the slopes of CM and PQ to establish the perpendicularity.

The slope of PQ is calculated by (y2 - y1) / (x2 - x1), which gives us (-1 - 3) / (4 - (-2)) = -4 / 6 = -2 / 3. The slope of CM is found using the coordinates of M(1, 1) and C(-1, -2), which gives us (-2 - 1) / (-1 - 1) = -3 / -2 = 3 / 2.

The slopes of two perpendicular lines are negative reciprocals of each other. Since the slope of CM (3/2) is the negative reciprocal of the slope of PQ (-2/3), CM is therefore perpendicular to PQ.

User Gui Ferreira
by
7.5k points
2 votes

Step-by-step explanation:

hope it helps!!

sorry for the rough handwriting tho

The midpoint of the line segment joining P(-2, 3) and Q(4,-1) is M. The point C has-example-1
User CharanRoot
by
8.2k points

No related questions found

Welcome to QAmmunity.org, where you can ask questions and receive answers from other members of our community.

9.4m questions

12.2m answers

Categories