Question

Can someone help me understand this?
"the midpoint of uv is (5, -11). The coordinates of one endpoint are U(3, 5) find the coordinates of endpoint v"

Answer 1

y=mx+b

y=ΔyΔxx+b

y=y2−y1x2−x1x+b

y=(−11)−55−3x+b

y=−162x+b

y=−8x+b


substitute in a point to figure out b (I'll put U in).
5=(−8)(3)+b

5=−24+b

b=29


So the equation of you're line is:
y=−8x+29


Now the symmetry part:
The midpoint is +2 in the x direction, so add another 2 to the midpoint to get V's x coordinate.

y3=−8x3+29

y3=−8(7)+29

y3=−56+29

y3=−27


V should be (7, -27)

s=(Δy)2+(Δx)2−−−−−−−−−−−−√

s=(y2−y1)2+(x2−x1)2−−−−−−−−−−−−−−−−−−√

s=(−11−5)2+(5−3)2−−−−−−−−−−−−−−−−−√

s=(−16)2+(2)2−−−−−−−−−−−√

s=256+4−−−−−−√

s=260−−−√


midpoint to V

s=(Δy)2+(Δx)2−−−−−−−−−−−−√

s=(y3−y2)2+(x3−x2)2−−−−−−−−−−−−−−−−−−√

s=((−27)−(−11))2+(7−5)2−−−−−−−−−−−−−−−−−−−−−−√

s=(−16)2+(2)2−−−−−−−−−−−√

s=256+4−−−−−−√

s=260−−−√

Answer 2

If you have any questions here to help!

Answer 3

Okay thank you so much!(:

Answer 4

WOW

That seems a complicated explanation for a simple concept

The midpoint is middle of UV in both X and Y direction

SO

Find how far to move from end poit to midpoint in x then add the same amount again
Find out how far to move from endpoint ot midpoint in Y then add the same amount again.

(Note value to 'add' may be negative)