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The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is
a. (0, 1)
b. (0, –1)
c. (–1, 0)
d. (1, 0)

Solution:

Consider the fourth vertex as D = (x, y)

As the diagonals of a parallelogram bisect each other, the midpoint of AC is the same as the midpoint of BD.

We know that

The coordinates of the mid-point of the line segment joining the point are

[(x₁ + x₂)/2, (y₁ + y₂)/2]

As the midpoint of AC = Midpoint of BD

[(-2 + 8)/2, (3 + 3)/2] = [(6 + x)/2, (7 + y)/2]

By further calculation

[6/2, 6/2] = [(6 + x)/2, (7 + y)/2]

Now we get

6 + x = 6

x = 6 - 6 = 0

And 7 + y = 6

y = 6 - 7 = -1

Therefore, the fourth vertex D is (0, -1).

✦ Try This: The fourth vertex S of a parallelogram PQRS whose three vertices are P (-4, 2), Q (4, 5) and R (9, 4) is

☛ Also Check: NCERT Solutions for Class 10 Maths Chapter 7

NCERT Exemplar Class 10 Maths Exercise 7.1 Problem 11

The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is a. (0, 1), b. (0, –1), c. (–1, 0), d. (1, 0)

Summary:

The fourth vertex D of a parallelogram ABCD whose three vertices are A (–2, 3), B (6, 7) and C (8, 3) is (0, -1)

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