Y is a the midpoint of XZ. For each pair of points given, find the coordinates of the third point.
(Im not sure how to work this out, any help would be grateful)
X(5,5), Z(-1,5)
Y(_____,_____)
Z(2,8), Y(-2,2)
X(_____,_____)
Y = ((5-1)/2,(5+5)/2) = (2,5)
(-2,2) = ((X1+2)/2,(X2+8)/2)
So, X = (-6,-4)
To find the coordinates of the third point, Y, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint, M, between two points (x₁, y₁) and (x₂, y₂) is given by:
M(x, y) = ((x₁ + x₂) / 2, (y₁ + y₂) / 2)
Let's apply this formula to each pair of points:
1. For X(5, 5) and Z(-1, 5):
Using the formula, we have:
Y(x, y) = ((5 + (-1)) / 2, (5 + 5) / 2)
= (4 / 2, 10 / 2)
= (2, 5)
Therefore, Y is (2, 5).
2. For Z(2, 8) and Y(-2, 2):
Using the formula, we have:
X(x, y) = ((2 + (-2)) / 2, (8 + 2) / 2)
= (0 / 2, 10 / 2)
= (0, 5)
Therefore, X is (0, 5).
So, the coordinates of each third point are:
Y(2, 5)
X(0, 5)
To find the coordinates of the third point, Y, given that Y is the midpoint of XZ, you can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint of a line segment, (x1, y1) and (x2, y2), are the average of the corresponding coordinates.
For the first pair of points, X(5, 5) and Z(-1, 5), we can use the midpoint formula to find the coordinates of Y.
1. Find the average of the x-coordinates:
(5 + -1) / 2 = 4 / 2 = 2
So, the x-coordinate of Y is 2.
2. Find the average of the y-coordinates:
(5 + 5) / 2 = 10 / 2 = 5
So, the y-coordinate of Y is 5.
Therefore, Y(2, 5).
For the second pair of points, Z(2, 8) and Y(-2, 2), we can again use the midpoint formula to find the coordinates of X.
1. Find the average of the x-coordinates:
(2 + -2) / 2 = 0 / 2 = 0
So, the x-coordinate of X is 0.
2. Find the average of the y-coordinates:
(8 + 2) / 2 = 10 / 2 = 5
So, the y-coordinate of X is 5.
Therefore, X(0, 5).
To recap:
- For the first pair of points, X(5, 5) and Z(-1, 5), Y is the midpoint. Therefore, Y(2, 5).
- For the second pair of points, Z(2, 8) and Y(-2, 2), X is the midpoint. Therefore, X(0, 5).