1.
In which quadrant does the point(-4, -7) lie?
Answer: Option 'C'
The point (-4, -7) lies in 3rd quadrant.
2.
In which quadrant does the point(1, 5) lie?
Answer: Option 'A'
The point (1, 5) lies in 1st quadrant.
3.
In which quadrant does the point(9, -2) lie?
Answer: Option 'D'
The point (9, -2) lies in 4th quadrant.
4.
In which quadrant does the point(-7, 6) lie?
Answer: Option 'B'
The point (-7, 6) lies in 2nd quadrant.
5.
In which quadrant does the point(0, 9) lie?
Answer: Option 'B'
Answer: Option 'B'
The point (0, 9) lies in x-axis.
6.
In which quadrant does the point(9, 0) lie?
Answer: Option 'A'
The point (9, 0) lies in y-axis.
7.
Find the distance of the point A(4, -4) from the origin.
Answer: Option 'D'
OA = √42+(-4)2 = √16+16 = √32 = 8√2
8.
Find the distance of the point A(3, -3) from the origin.
Answer: Option 'A'
OA = √32+(-3)2 = √9+9 = √18 = 3√2
9.
P is a point on x-axis at a distance of 4 units from y-axis to its right. The co-ordinates of P are:
Answer: Option 'A'
The co-ordinates of P are A(4, 0)
10.
A is a point on y-axis at a distance of 5 units from x-axis lying below x-axis. The co-ordinates of A are:
Answer: Option 'D'
The co-ordinates of A are A(0, -5)
11.
Find the distance of the point A(4, -2) from the origin.
Answer: Option 'B'
OA = √4 - 02+(-2 - 0)2 = √16+4 = √20 = √4 × 5 = 2√5 units
12.
Find the distance between the points A(-4, 7) and B(2, -5).
Answer: Option 'B'
AB = √(2+4)2 + (-5-7)2
= √62 + (-12)2
= √36+144 = √180
=√36 × 5 = 6√5 units.
13.
The distance between the points A(b, 0) and B(0, a) is.
Answer: Option 'B'
AB = √(b-0)2-(0-a)2
= √b2+a2
= √a2+b2.
14.
If the distance of the point P(x, y) from A(a, 0) is a + x, then y2 = ?
Answer: Option 'C'
√(x-a)2+(y-0)2 = a + x
= (x-a)2+y2
= (a+x)2 => y2 = (x-a)2-(x-a)2-4ax => y2 = 4ax
15.
The distance between the points A(5, -7) and B(2, 3) is:
Answer: Option ''
AB2 = (2 - 5)2 + (3 + 7)2
=> (-3)2 + (10)2
=> 9 + 100 => √109
16.
Find the area of ΔABC whose vertices are A(9, -5), B(3, 7) and (-2, 4).
Answer: Option 'C'
Here, x1 = 9, x2 = 3, x3 = -2 and y1 = -5, y2 = 7, y3 = 4
= 1/2 [9(7-4) + 3(4+5) + (-2)(-5-7)]
= 1/2 [9(3) + 3(9) - 2(-12)]
= 1/2 [27 + 27 + 24]
= 1/2 [78]
= 39 sq.units
17.
Find the area of ΔABC whose vertices are A(2, -5), B(4, 9) and (6, -1).
Answer: Option 'D'
Here, x1 = 2, x2 = 4, x3 = 6 and y1 = -5, y2 = 9, y3 = -1
= 1/2 [2(9+1) + 4(-1+5) + 6(5-9)]
= 1/2 [2(10) + 4(4) + 6(-4)]
= 1/2 [20 + 16 - 24]
= 1/2 [12]
= 6 sq.units
18.
The points A(0, 6), B(-5, 3) and C(3, 1) are the vertices of a triangle which is ?
Answer: Option 'C'
AB2= (-5 - 0)2 + (-3 - 0)2 = 16 + 9 = 25
BC2 = (3 + 5)2 + (1-3)2 = 82 + (-2)2 = 64 + 4 = 68
AC2 = (3 - 0)2 + (1 - 6)2 = 9 + 25 = 34.
AB = AC. ==> ΔABC is isosceles.
19.
The points A(-4, 0), B(1, -4), and C(5, 1) are the vertices of
Answer: Option 'A'
AB2 = (1 + 4)2 + (-4 - 0)2
= 25 + 16 = 41,
BC2 = (5 - 1)2 + (1 + 4)2 = 42 + 52
= 16 + 25 = 41
AC2 = (5 + 4)2 + (1 - 0)2
= 81 + 1 = 82
AB = BC and AB2 = BC2 = AC2
ΔABC is an isosceles right angled triangle
20.
Find the vertices of triangle are A(2, 8), B(-4, 3) and (5, -1). The area of ΔABC is:
Answer: Option 'C'
Here, x1 = 2, x2 = -4, x3 = 5 and y1 = 8, y2 = 2, y3 = -1
= 1/2 [2(3+1) - 4(-1-8) + 5(8-3)]
= 1/2 [2(4) + 4(-9) + 5(5)]
= 1/2 [16 - 36 + 25]
= 1/2 [5]
= 2 1/2 sq.units