Find the midpoint M of the line segment joining the points C = (-4, 4) and D = (8, -6).
Answer (1)
To find the midpoint M of the line segment joining the points C = ( − 4 , 4 ) and D = ( 8 , − 6 ) , you can use the midpoint formula.
The midpoint formula is:
M = ( 2 x 1 + x 2 , 2 y 1 + y 2 )
Here, ( x 1 , y 1 ) represents the coordinates of the first point C = ( − 4 , 4 ) and ( x 2 , y 2 ) represents the coordinates of the second point D = ( 8 , − 6 ) .
Using these values, plug them into the formula:
M = ( 2 − 4 + 8 , 2 4 + ( − 6 ) )
Calculate each part separately:
For the x-coordinate: 2 − 4 + 8 = 2 4 = 2
For the y-coordinate: 2 4 + ( − 6 ) = 2 − 2 = − 1
So the midpoint M is ( 2 , − 1 ) .
The midpoint M of the line segment between the points C and D is ( 2 , − 1 ) . This point is exactly halfway between the two given points on the plane, meaning it balances the line segment equally in terms of both the x and y coordinates.
