Area of Triangle Given Its Vertices

Q.

The points (5, - 2), (6, 4) and (7, - 2) are the vertices of an _________ triangle.

Q. Question 10
The point A(-6, 10), B(-4, 6) and C(3, -8) are collinear such that $AB=\frac{2}{9}AC.$

Q. Question 7
The area of a triangle with vertices A(3, 0), B(7, 0) and C(8, 4) is
(A) 14
(B) 28
(C) 8
(D) 6

Q. Question 2 (ii)
Find the value of 'k', for which the following points are collinear.
(ii) (8, 1), (k, -4), (2, -5)

Q.

If the coordinates of two points A and B are (3, 4) and (5, – 2) respectively. Find the coordinates of any point P, if PA = PB and area of $△$PAB = 10

Q. P(x, y), A(3, 4) and B (5, -2) are the vertices of triangle PAB such that |PA|=|PB| and area of $\Delta PAB=10$ sq. units, then $PA=k\sqrt{5}$ units. Find the value of k.

1. 2
2. $\sqrt{5}$
3. 1
4. 3

Q. Question 6
Find the coordinates of the point Q on the X-axis which lies on the perpendicular bisector of the line segment joining the points A(-5, -2) and B(4, -2). Name the type of triangle formed by the point Q, A and B.

Q. The co-ordinates (5, - 2), (6, 4) and (7, - 2) are the vertices of an isosceles triangle.

1. False
2. True

Q.

A question was asked in a class
”The points A(5, 5), B(4, 4) and C(3, 3) form which triangle?”.
Unfortunately, no student could get it right.
What type of triangle will be formed if the points are joined ?

1. Scalene

2. Isosceles

3. The three points do not form a triangle.

4. Right angled

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

Q. Question 5
The points A(3, 1), B(12, -2) and C(0, 2) cannot be vertices of a triangle.

Q. Question 4
Find the area of the quadrilateral whose vertices, taken in order, are (-4, -2), (-3, -5), (3, -2) and (2, 3).

Q.

Refer to the following figure. If we were given the coordinates of A, E and B and the lengths of ED, DC and BC, how would you go about finding the area of this figure, pick the easiest way.

1. Break the fig. into ΔAEB and trapezium EBCD

2. Break the fig. into ΔAEB, ΔEAB and ΔBDC

3. Break the fig. into trapeziums EDAX and AXCB where X is
   a point on DC such that AX is perpendicular to AX.

4. Cant say

Q.

Find the area of the figure:

1. 24
2. 25
3. 26
4. 27

Q. Find the value of m if the points A (5, 1), B(-2, -3) and C(8, 2m) are collinear
m= _
(Enter in the form a/b if you obtain a fraction)

Q.

Find the value of m if the points A(5, 1), B(-2, -3) and C(8, 2m) are collinear
m = ___
(Enter in the form a/b if you obtain a fraction)

Q.

The area of a quadrilateral whose vertices taken in order are (–4, –2), (–3, –5), (3, –2) and (2, 3) is _______.

1. 26 sq. units

2. 30 sq. units

3. 28 sq. units

4. 27 sq. units

Q.

What is the area of a triangle whose vertices are (a , b + c), (a, b - c) and (-a, c)?

1. 4ac

2. 2ab

3. 2ac

4. 4ab

Q.

The area of a triangle is 5 square units. Two of its vertices are (2, 1) and (3, -2) and the third vertex lies on y = x + 3, the third vertex is

1. $(3,4)$

2. $(\frac{5}{2}$, $\frac{13}{2})$

3. $(\frac{7}{2}$, $\frac{13}{2})$

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

Q.

What is the area of this trapezium?

ED and BC are perpendicular to DC. ED = a, BC = b, DC = c

1. (1/2)(c+b)(b+a)

2. (1/2)c(a+b)

3. (1/2)a(c+b)

4. (1/2)b(c+a)

Q. The triangle formed by the points (3, 5), (6, 9), and (2, 6) is

1. equilateral
2. isosceles
3. right-angled
4. scalene

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

Q. What is the area of the right-angled triangle $\Delta MNO$, right angled at N.

1. $\frac{1}{2}\times MN\times NO$
2. $\frac{1}{2}\times MN\times MO$
3. $\frac{1}{2}\times MO\times NO$
4. $MN\times NO$

Q. If the area of the triangle formed by the points A(a, 3), B(5, 2) and C(c, 3) is 4, then the length of the side AC is ___.

Q.

The area of a triangle having vertices (a, b+ c), (b, c + a) and (c, a + b) is ___.

1. 0

2. $a^2$ + $b^2$ + $c^2$

3. 1

4. a + b + c

Q. Let ABCD be a quadrilateral with area 18, with side AB parallel to the side CD and AB = 2 CD. Let AD be perpendicular to AB and CD. If a circle is drawn inside the quadrilateral ABCD touching all the side, then its radius is

1. 3
2. 2
3. $\frac{3}{2}$
4. 1

Q.

If 2 triangles have the same height, the ratio of their areas is equal to the

1. Ratio of heights

2. 1

3. Ratio of any 2 sides

4. Ratio of corresponding bases