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Points A(-2, 4, 8(1.3), C(4, -1) and D form a parallelogram. What are the coordinates of D9

Points A(-2, 4, 8(1.3), C(4, -1) and D form a parallelogram. What are the coordinates-example-1
User Frangulyan
by
6.4k points

1 Answer

5 votes

Answer:

D. (1, 0)

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

Points A(-2, 4, 8(1.3), C(4, -1) and D form a parallelogram. What are the coordinates-example-1
Points A(-2, 4, 8(1.3), C(4, -1) and D form a parallelogram. What are the coordinates-example-2
Points A(-2, 4, 8(1.3), C(4, -1) and D form a parallelogram. What are the coordinates-example-3
User Sheldon Rong
by
5.0k points
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