The midpoint of ab is M=(-4,0). one endpoint i A=(-6,2). find the coordinates of the of the other endpoint, B
To find the coordinates of endpoint B, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint (M) is equal to the average of the coordinates of the endpoints (A and B).
Let's denote the coordinates of endpoint B as (x, y).
According to the midpoint formula, we have the following equations:
(Midpoint x-coordinate) = (Endpoint A x-coordinate + Endpoint B x-coordinate) / 2
-4 = (-6 + x) / 2 [Substituting the given values]
Now, let's solve the equation for x:
-4 = (-6 + x) / 2
-4 * 2 = -6 + x
-8 = -6 + x
-8 + 6 = x
-2 = x
So, the x-coordinate of endpoint B is -2. Now, let's find the y-coordinate.
(Midpoint y-coordinate) = (Endpoint A y-coordinate + Endpoint B y-coordinate) / 2
0 = (2 + y) / 2 [Substituting the given values]
Solving the equation for y:
0 = (2 + y) / 2
0 * 2 = 2 + y
0 = 2 + y
-2 = y
Therefore, the coordinates of endpoint B are (-2, -2).
Calculate the distance between the points K=(-6,-5) And M=(-3,2) in the coordinate plane. Give and exact answer ( not a decimal approximation)
To calculate the distance between two points in a coordinate plane, we can use the distance formula.
The distance formula states that the distance between two points with coordinates (x1, y1) and (x2, y2) is given by:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's use this formula to calculate the distance between K=(-6, -5) and M=(-3, 2).
Let x1 = -6, y1 = -5, x2 = -3, and y2 = 2.
Distance = √((-3 - (-6))^2 + (2 - (-5))^2)
= √((-3 + 6)^2 + (2 + 5)^2)
= √(3^2 + 7^2)
= √(9 + 49)
= √58
Therefore, the exact distance between points K=(-6, -5) and M=(-3, 2) is √58.
To find the coordinates of the other endpoint B, we need to use the midpoint formula. The midpoint formula states that the midpoint of a line segment is the average of the coordinates of its endpoints.
Let's denote the coordinates of the other endpoint B as (x, y).
According to the midpoint formula, we can calculate the x-coordinate of B using the formula:
(x-coordinate of A + x-coordinate of B) / 2 = x-coordinate of M
Substituting the known values, we have:
(-6 + x) / 2 = -4
Multiply both sides of the equation by 2:
-6 + x = -8
Add 6 to both sides of the equation:
x = -2
Now, let's calculate the y-coordinate of B using the formula:
(y-coordinate of A + y-coordinate of B) / 2 = y-coordinate of M
Substituting the known values, we have:
(2 + y) / 2 = 0
Multiply both sides of the equation by 2:
2 + y = 0
Subtract 2 from both sides of the equation:
y = -2
Therefore, the coordinates of the other endpoint B are (-2, -2).