We want to find the coordinates of a point D such that AB is parallel to CD.
The coordinates of D are: D (10, 7).
We have that:
- A(1, 7)
- B(8, 4)
- C(3, 10)
- D(x, y).
If we want CD to be parallel to AB, then the change in the components between D and C must be the same as the change in the components between B and A.
The change in the x-component between B and A is:
8 - 1 = 7
The change in the y-component between B and A is:
4 - 7 = -3
Then the coordinates of D are given by:
x = 3 + 7 = 10
y = 10 + (-3) = 7
The coordinates of D such that CD is parallel to AB are:
D(10, 7).
Notice that this is just an option, there are a lot of other possible coordinates that will also make CD parallel to AB, this is just the easier one to find.
If you want to learn more, you can read:
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