Coordinates of a Parallelogram

Q.

In parallelogram PQRS, P(-3, 2), Q(2, 7) and S(1, 9) are three vertices. Then the length of diagonal PR is

1. $\sqrt{100}$ units

2. $\sqrt{122}$ units

3. $\sqrt{167}$ units

4. $\sqrt{181}$ units

Q.

In the following figure A, B, C are the midpoints of the sides of $△PQR$. If A, B and Q has the coordinates (3, 3), (4, 2) and (2, 1) respectively, then the coordinates of P, C and R are

1. (5, 4), (4, 5) and (4, 3)

2. (6, 5), (5, 7) and (6, 3)

3. (4, 5), (5, 4) and (6, 3)

4. (3, 5), (5, 6) and (4, 3)

Q.

In parallelogram ABCD, A(-5, 2), B(1, 3) and D(-2, 10). Then the coordinates of C is

1. (1, 10)

2. (1, 11)

3. (4, 10)

4. (4, 11)

Q.

In parallelogram ABCD, A(2, 3), B(7, 3) and D(4, 7). Then the coordinates of C is

1. (9, 4)

2. (4, 9)

3. (9, 7)

4. (7, 9)

Q.

In parallelogram ABCD, A(3, 2), B(8, 4) and D(5, 7). Then the coordinates of C is

1. (9, 8)

2. (10, 9)

3. (9, 10)

4. (8, 9)

Q. In parallelogram ABCD, A(2, 3), B(6, 5) and D(4, 7). Then the coordinates of C is

1. (4, 2)
2. (8, 9)
3. (8, 7)
4. (4, 9)

Q.

In parallelogram ABCD, A(0, -7), B(5, -7) and D(2, -2). Then the coordinates of C are

1. (7, -2)

2. (7, -3)

3. (6, -2)

4. (6, -3)

Q.

The vertices of $\Delta ABC=areA(4,6),B(1,5)andC(7,2)$. A line is drawn to intersect sides AB and AC at D and E respectively such that $\frac{AD}{AB}=\frac{AE}{AC}=\frac{1}{4}$ . Calculate the area of $\Delta ADE$ and compare it with the area of $\Delta ABC$

Q.

The points A(1, 2), B(4, 3), C(1, 0) and D(-2, -1) are the vertices of a parallelogram. “The midpoints of AC and BD are the same.”

1. True
2. False

Q.

In parallelogram PQRS, P(-3, 2), Q(2, 7) and S(1, 9) are three vertices. Then the length of diagonal PR is

1. 25 units
2. 15 units
3. 12 units
4. 9 units

Q.

In parallelogram ABCD, A(2, 3), B(6, 5) and D(4, 7). Then the coordinates of C is

1. (4, 2)

2. (4, 9)

3. (8, 9)

4. (8, 7)

Q. If the points A(1, 2), B(4, 3), C(1, 0) and D(p, -1) are the vertices of a parallelogram then, find the value of p.

1. 3
2. 4
3. 0
4. -2

Q.

In parallelogram ABCD, A(1, 3), B(5, 3) and D(3, 8). Then the coordinates of C are

1. (5, 8)

2. (7, 8)

3. (6, 8)

4. (8, 7)