Given the following two end points for the line AB, find the distance between A and midpoint (see Q's below)

Question

1. A(-7,-7) and B (-7,-4) 2. A(9,-6) and B(5,-6)
3. A(7,1) and B(10,1) 4. A(-1,-7) and B(-1,-2)
5.(A(9,-4) and B(10,1) 6. A (16, -10) and B(1,-12)

If you could show some of the steps for these it would be appriciated. To those who answer 1/2 I'll award 4/5 stars. To those who answer all of these, I'll award you a best answer and 5/5 stars.

Answer 1

1. The mid point is -7,-51/2 now use pythagoran theorem betwwen A and the mid point
D^2 = (-7 +7)^2+ (-4+5.5)^2
D^2= 0 +2.25
D=1.5

All of these work the same: get the average of the x and y of the end points and that will be the mid point. Then use pythagoran theorem from midpoint to end point(A)

Answer 2

#1
A(-7, -7)
B(-7, -4)

(A + B) / 2
= (ax + bx, ay + by) / 2
= (-7 + -7, -7 + -4) / 2
= (-14, -11) / 2
= (-7, -5.5) this is the midpoint of the line

Midpoint - A
(-7, -5.5) - (-7, -7)
= (0, 1.5)

Therefore the distance from A to the midpoint for question 1 is 1.5.

** The same principles apply to all questions here.

Answer 3

1. midpoint = ((-7+(-7))/2, (-7+(-4))/2)= (-7, -5.5)
Distance = sqrt((-5.5-(-7)^2 + (-7-(-7))^2)= sqrt (2.25)=1.5

2. midpoint = ((9+5)/2, ((-6+-6)/2)=(7, -6)
D = sqrt((7-9))^2 + (-6-(-6))^2) = 2

3.midpoint = (17/2, 1)
D = sqrt((17/2-7)^2 + (1-1)^2) = 1.5

4. midpoint = (-1, -4.5)
D = ((-4.5-(-7)^2+ (-1-(-1) = 2.5

5. midpoint = (19/2, -3/2)
D= sqrt((19/2-9)^2 + (-3/2 -(-4)^2)
= sqrt((.5)^2 + 2.5^2) = sqrt(6.5)

6. midpoint = (17/2, -11/2) =(8.5,-5.5)
D= sqrt((8.5-16)^2 + (-5.5- (-10))^2
= sqrt((-7.5)^2 + (4.5)^2) = sqrt (76.5)