a(1,7),b(-3,1) coordinates of missing endpoint if b is the midpoint of ac
-7,-5
How do you solve this?
To find the missing endpoint, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Given that point B is the midpoint of AC, and the coordinates of B are (-3, 1), we can substitute the coordinates of B into the midpoint formula along with the coordinates of A, and find the missing endpoint C.
Let's denote C as (x, y).
Using the midpoint formula:
((-3 + x) / 2, (1 + y) / 2) = ((1 + 7) / 2, (-3 + 1) / 2)
Simplifying:
((-3 + x) / 2, (1 + y) / 2) = (8 / 2, -2 / 2)
((-3 + x) / 2, (1 + y) / 2) = (4, -1)
Now, set the x-coordinate and y-coordinate equal to each side of the equation to solve for x and y separately:
(-3 + x) / 2 = 4 --> -3 + x = 8 --> x = 11
(1 + y) / 2 = -1 --> 1 + y = -2 --> y = -3
Therefore, the missing endpoint C is (11, -3).
To find the missing endpoint of a line segment where one endpoint and the midpoint are given, we can use the midpoint formula.
The midpoint formula states that the coordinates of the midpoint of a line segment with endpoints (x1, y1) and (x2, y2) are given by the following formulas:
midpoint x-coordinate = (x1 + x2) / 2
midpoint y-coordinate = (y1 + y2) / 2
In this case, we are given the coordinates of point B, which is the midpoint of the line segment AC. Let's denote the coordinates of point A as (x1, y1) and the coordinates of the missing endpoint C as (x2, y2).
Given:
Point B: (-3, 1)
Point A: (1, 7)
We can substitute these values into the midpoint formula to find the missing endpoint C:
midpoint x-coordinate = (x1 + x2) / 2
midpoint y-coordinate = (y1 + y2) / 2
Substituting the known values:
-3 = (1 + x2) / 2
1 = (7 + y2) / 2
Now, let's solve these equations to find the values of x2 and y2.
-3 = 1 + x2
x2 = -3 - 1
x2 = -4
1 = 7 + y2
y2 = 1 - 7
y2 = -6
Therefore, the missing endpoint C has the coordinates (-4, -6).