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

try to understand, you need not give any stars
if the coordinates of end points are (x1,y1) and (x2, y2)
then the co ordinates of mid point are
x3 = (x1+x2)/2
y3 = (y1 + y2)/2
distance between two points(x1, y1) and (x2, y2) is
sqrt[(x2 - x1)^2 + (y2 - y1)^2]
1)
here coordinates of A
x1 =-7, y1 = -7
coordinates of B
x2 =-7, y2 = -4
coordinates of midpoint of AB
x3 = -7 + (-7)/2 = -14/2 = -7
y3 = -7 + (-4)/2 = (-7 - 4) = -11/2
distance between A(-7, -7) and (-7, -11/2)
sqrt[(-7-(-7)^2 + (-11/2 - (-7))^2]
sqrt(0 + (3/2)^2]
sqrt(9/4) = 3/2 units
2)
mid point = (7, -6)
distance between A nd mid point
sqrt(9-7)^2 + 0) = sqrt(4) = 2 units
3)
mid point = (17/2, 1)
distance = sqrt[(7 - 17/2)^2 + (1-1)^2]
= sqrt(9/4) = 3/2 units
4)
mid point = (-1, -9/2)
distance =
sqrt[(0+(-7 - (-9/2))^2] = sqrt[25/4] = 5/2 units
5)
mid point = (19/2, -3/2)
distance = sqrt[(9-19/2)^2 + (-4 +3//2)^2]
srt(1/4 + 25/4) = sqrt(26/4) = sqrt(13)/2
6)
mid point = (17/2, -11)
distance = sqrt[(16- 17/2)^2 + (-10 +11)^2]
=sqrt(225/4 + 1) = sqrt(229/4) = sqrt(229)/2 units

Answer 2

The trick here is to use Pythagorean's Theorem:
(a^2) + (b^2) = (c^2) where c is the hypotenuse (the longest side of a triangle). In the case of these problems, you can imagine that the hypotenuse is the line between the two points given (line AB). One side of the triangle (a) will be the length in the x direction and the other side (b) will be the length in the y direction. Once you find a and b you can solve for c, which is the entire length of line AB. Since the distance between A and the midpoint is half the lenght of AB, all you have to do is divide the length of AB by 2. In order to find a, all you need to do is subtract the x coordinate of B from the x coordinate of A. Likewise, in order to find b, all you have to do is subtract the y coordinate of B from the y coordinate of A. Here's how to do some of the problems:

1. A(-7, -7) and B(-7, -4)
a = -7 - (-7) = -7+7 = 0
b = -7 - (-4) = -7 +4 = -3 = 3(no such thing as negative distance, so just make it positive)
(c^2) = (a^2) + (b^2)
= (0^2) + (3^2)
= 0 + 9 = 9
c = sqr rt (9) = 3 <<< You may notice that the lenght of c is the same as b. That is because this is a vertical line. If you were to plot the two point, you can see this easier (sorry, can't plot them for you!). When both x values are the same, you have a vertical line and when both y values are the same, you have a horizontal line. At that point, you don't really even need to use Pythagorean's Theorom. The length of the other line (a or b) will be the length of AB. Don't forget the that isn't the answer though. The distance from A to midpoint is half of the length of AB, so....
distance from A to midpoint = 3/2 = 1.5

Questions 2-4 are about the same, so I'm not going to show you those. Questions 5 & 6 aren't vertical or horizontal, so I'll show you 5.

5. A(9, -4) and B(10, 1)
a = 9 - 10 = -1 = 1
b = -4 - 1 = -5 = 5
(c^2) = (a^2) + (b^2)
= (1^2) + (5^2)
= 1 + 25 = 26
c = sqr rt (26) <<<<<< distance from A to midpoint: (sqr rt (26))/2
you can calculate the decimal value if you'd like.

Hope this helps!!

Answer 3

#a million A(-7, -7) B(-7, -4) (A + B) / 2 = (ax + bx, ay + via) / 2 = (-7 + -7, -7 + -4) / 2 = (-14, -11) / 2 = (-7, -5.5) it fairly is the midpoint of the line Midpoint - A (-7, -5.5) - (-7, -7) = (0, a million.5) as a result the gap from A to the midpoint for question a million is a million.5. ** the comparable innovations be conscious to all questions here.

Answer 4

first you need to get the coordinates of the midpoint before you can get the distance from A to the midpoint. formula for getting the coordinates of the midpoint is;
X = (X1 + X2)/2 ; Y = (Y1 + Y2)/2
then to get the distance use distance formula let point A = P1 and the midpoint=P2
d= sqrt of [(X2 - X1)^2 + (Y2 - Y1)^2]

Answer 5

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