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QuestionFind the midpoint of line segment AB where A is (-7,4) and B is (3,-4).

Studdy Solution

STEP 1

Assumptions1. We are given two points A and B in the plane. . The coordinates of point A are (-7,4).
3. The coordinates of point B are (3,-4).
4. We need to find the midpoint of the line segment AB.

STEP 2

The formula to find the midpoint M of a line segment with endpoints A(x1, y1) and B(x2, y2) is given byM=(x1+x22,y1+y22)M = \left(\frac{x1 + x2}{2}, \frac{y1 + y2}{2}\right)

STEP 3

Plug in the given values for the coordinates of points A and B into the midpoint formula.
M=(−7+32,+(−)2)M = \left(\frac{-7 +3}{2}, \frac{ + (-)}{2}\right)

STEP 4

Calculate the x-coordinate of the midpoint M.
Mx=−7+32=−42=−2M_x = \frac{-7 +3}{2} = \frac{-4}{2} = -2

STEP 5

Calculate the y-coordinate of the midpoint M.
My=4+(−4)2=02=0M_y = \frac{4 + (-4)}{2} = \frac{0}{2} =0

STEP 6

Now that we have the x and y coordinates of the midpoint M, we can write the coordinates of M.
M=(−2,0)M = (-2,0)The midpoint of the line segment AB is (-2,0).

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