have a question in math
(( distance between two points ))
show that C(-5,-1)is the midpoint of the line segment joining A(-2,5) and B(-8,-7)
please in detales .. thank u
To show that point C(-5,-1) is the midpoint of the line segment joining A(-2,5) and B(-8,-7), we need to examine two things: the coordinates of the midpoint and the distance between each point and the midpoint.
The coordinates of the midpoint can be found using the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's calculate the midpoint:
Midpoint = ((-2 + -8) / 2, (5 + -7) / 2)
= (-10/2, -2/2)
= (-5, -1)
Now, let's calculate the distance between each point (A and B) and the midpoint (C) using the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
For point A:
Distance_A-C = √((-5 - (-2))^2 + (-1 - 5)^2)
= √((-5 + 2)^2 + (-1 - 5)^2)
= √((-3)^2 + (-6)^2)
= √(9 + 36)
= √45
= 6.708
For point B:
Distance_B-C = √((-5 - (-8))^2 + (-1 - (-7))^2)
= √((-5 + 8)^2 + (-1 + 7)^2)
= √((3)^2 + (6)^2)
= √(9 + 36)
= √45
= 6.708
Now we can see that the distance from A to C and the distance from B to C are both equal to 6.708, confirming that C(-5,-1) is indeed the midpoint of the line segment joining A(-2,5) and B(-8,-7).