Application of Mid Point Formula

Q.

ABC is a triangle and G(4, 3) is the centroid of the triangle. If A = (1, 3), B = (4, b) and C = (a, 1). Then the length of side BC is:

1. 10 units

2. 5 units

3. 15 units

4. 25 units

Q.

Three vertices of a parallelogram ABCD taken in order are A(3, 6), B (5, 10) and C(3, 2). Then the coordinates of the fourth vertex D is

1. (1, -2)

2. (-1, 2)

3. (2, -1)

4. (-2, 1)

Q.

If $(1,2),(4,y),(x,6)$ and $(3,5)$ are the vertices of parallelogram taken in order, find $x$ and $y$.

1. $(6,3)$

2. $(4,3)$

3. $(2,5)$

4. $(2,3)$

Q.

If the vertices of a triangle are (a, 1), (b, 3) and (4, c), then the centroid of the triangle will lie on the x-axis, if

1. c = -4

2. b + c = -4

3. a + c = -4

4. a + b = -4

Q.

If A (1, 2), B (4, y), C (x, 6) and D (3, 5) are vertices of a parallelogram ABCD, find the values of x and y. [4 MARKS]

Q. Find the area of the triangle formed by joining the midpoints of the sides of the triangle formed with coordinates A (-4, 3), B (2, 3) and C (4, 5) is sq. units.

1. 2 sq. units.
2. 0.5 sq. units.
3. 1 sq. units.
4. 1.5 sq. units.

Q.

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex.

Q. Find the point that divides A(2, 4) and B(6, 8) in the ratio a : 1.

1. $(\frac{6a+1}{a+1},\frac{8a+4}{a+1})$
2. $(\frac{6a+2}{a+1},\frac{8a+4}{a+1})$
3. $(\frac{6+2a}{a+1},\frac{8+4a}{a+1})$
4. $(\frac{6a+8}{a+1},\frac{2a+4}{a+1})$

Q. What is the condition for three sides AB, BC and AC to form a triangle?

1. AC+BA>BC
2. AC+BC>AB
3. All of these
4. AB+BC>AC

Q.

If a vertex of a triangle is (1, 1) and the mid-points of the two sides through this vertex are (-1, 2) and (3, 2), then the centroid of the triangle is _____.

1. $(-1,\frac{7}{3})$

2. $(-\frac{1}{3},\frac{7}{3})$

3. $(1,\frac{7}{3})$

4. $(\frac{1}{3},\frac{7}{3})$

Q.

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). The third vertex is

1. (2, 10).

2. (-10, 2).

3. (2, -10).

4. (10, -2)

Q.

The centroid of the triangle whose vertices are (1, 3) (2, 7) and (12, -16) is

1. (-5 , 2)

2. (-5 , -2)

3. (5 , -2)

4. (5 , 2)

Q.

Two vertices of a triangle are (3, –5) and (–7, 4). If its centroid is (2, –1). Find the third vertex.

1. (12, -2)

2. (10, -2)

3. (9, -2)

4. (10, -3)

Q.

The points A(-a, b), B(-a, c) and C(a, c) form the vertices of a triangle. Which of the following is true?

1. Area of the triangle = b(a - c)
2. $\Delta ABC$ is a right angled triangle, right angled at A.
3. The triangle is equilateral.
4. Area of the triangle = a(c - b)