Question 21
Question: A median of a triangle divides it into two triangles of equal areas. Verify this result for 
ABC. Whose vertices are A (4, -6), B (3, -2) and C (5, 2). [3 Mark]
Answer: 
ABC is a triangle, AD is a median. i.e. D is the mid point BC. D (4, 0)
We have to verify that,
Area of 
ABD = area of 
ADC.
Area of 
ABD = 
= 3 Sq. units
Area of 
ADC = 
= 3 Sq. units
Thus it is verified thatarea of 
ABD = area of 
ADC
Question 22
Question: Find the length of the altitude of the triangle, whose vertices are (5, 1), (2, 4) and (- 1, -1). [3 Mark]
Answer: 
Area of 
ABC = 
= 12 Sq. units
Area of 
ABC = 
x base x height = 12 Sq. units
Length of AB = 
units
Length of BC = 
units
Length of CA = 
units
Altitude AD = 
units
Altitude BE = 
units
Altitude CF = 
units.
Question 23
Question: For what value of 'x' will the points (x, 3), (-5, 6) and (-8, 8) be collinear? [2 Mark]
Answer: Let the points be A(x, 3), B (-5, 6) and C (-8, 8).
To prove A, B, C are collinear, we have to equate the area of 
ABC to zero.
Area of 
ABC = 
= 0
= 
= 0
= 
= 0 
2x + 1 = 0 
x =
.
Question 24
Question: The co-ordinates of A, B and C are (6, 3), (-3, 5) and (4, -2) respectively and P is any point (x, y). Show that the ratio of the areas of triangles PBC and ABC is
. [2 Mark]
Answer: 
= 
= 
Question 25
Question: For what value of 'x', the area of the triangle formed by the points (5, -1), (x, 4) and (6, 3) is 5.5 Sq. units. [2 Mark]
Answer: Let A (5, -1), B (x, 4) and C (6, 3) be the vertices of 
ABC.
Area of 
ABC is equal to 5.5 or 
Sq. units.
4x -25 = 11
4x = 36
x = 9.
