Answer:
D. (1, 0)
Step-by-step explanation:
Mark the given points in the coordinate system (look at the picture).
Find the point D.
Other solutions:
D(-5, 8)
D(7, -2)
Look at the other pictures
If you want calculate it, then:
The vectors AB and DC are congruent and the vectors BC and AD are congruents too.
If a vector ,< a, b > is congruent to a vector < c, d >, then a = c and b = d.
The formula of coordinates of the vetror:
< x₂ - x₁, y₂ - y₁ >
We have A(-2, 4), B(1, 3), C(4, -1) and D(x, y). Substitute:
vector AB = < 1 - (-2), 3 - 4 > = < 3, -1 >
vector DC = < 4 - x, -1 - y >
vector BC = < 4 - 1, -1 - 3 > = < 3, -4 >
vector AD = < x - (-2), y - 4 > = < x + 2, y - 4 >
Therefore we have the equations:
AB = DC ⇒ 4 - x = 3 and -1 - y = -1 ⇒ x = 1 and y = 0
BC = AD ⇒ x + 2 = 3 and y - 4 = -4 ⇒ x = 1 and y = 0
