Answer:
9. The coordinates at the midpoint is (8,6)
10. The coordinates at Point U is (2,0)
Explanation:
Midpoint is the halfway of a line segment to another line.
To calculate the midpoint of line M(6,6) and R(10,6)
Use this formula
Midpoint (x,y) = (x1 + x2)/2 , (y1+y2)/2
At point M, x1 = 6 and y1 = 6
At point R, x2 = 10 and y2 = 6
Midpoint M(x,y) = (6+10)/2,(6+6)/2
= 16/2, 12/2
M(x,y) = (8,6)
Hence, the midpoint M = (8,6)
10.
The midpoint M (x,y) = (6,4)
Point U = (10,8)
Point T = Unknown
Using the formulation of midpoint, we can get the coordinates at point T
Remember that Midpoint (x,y) = (x1+x2)/2 , (y1+y2)/2
Where x = (x1+x2)/2
and
y = (y1+y2)/2
At point U,
x1 = 10, y1 = 8
At point T,
x2 and y2 are unknown
At the midpoint, M(x,y)
x = 6 , y = 4
Solving for x2 in x = (x1+x2)/2
6 = (10+x2)/2 ---------------Multiply both sides by 2
2 * 6 = 2 * (10+x2)/2
12 = 10 + x2 --------------- Collect like terms
12 - 10 = x2
2 = x2
x2 = 2
Solving for y2 in y = (y1+y2)/2
4 = (8 + y2)/2 ----------------- Multiply both sides by 2
2 * 4 = 2 * (8+y2)/2
8 = 8 + y2
8-8 = y2
0 = y2
y2 = 0
x2,y2 = (2,0)
So, the coordinates at Point U = (2,0)