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 - 0 ^{2}+(-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} **

= √b^{2}+a^{2}

= √a^{2}+b^{2}.

14.

If the distance of the point P(x, y) from A(a, 0) is a + x, then y^{2} = ?

**Answer: Option 'C'**

**√(x-a) ^{2}+(y-0)^{2} = a + x **

= (x-a)^{2}+y^{2}

= (a+x)^{2} => y^{2} = (x-a)^{2}-(x-a)^{2}-4ax => y^{2} = 4ax

15.

The distance between the points A(5, -7) and B(2, 3) is:

**Answer: Option ''**

**AB ^{2} = (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, x _{1} = 9, x_{2} = 3, x_{3} = -2 and y_{1} = -5, y_{2} = 7, y_{3} = 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, x _{1} = 2, x_{2} = 4, x_{3} = 6 and y_{1} = -5, y_{2} = 9, y_{3} = -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'**

**AB ^{2}= (-5 - 0)^{2} + (-3 - 0)^{2} = 16 + 9 = 25 **

BC^{2} = (3 + 5)^{2} + (1-3)^{2} = 8^{2} + (-2)^{2} = 64 + 4 = 68

AC^{2} = (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'**

**AB ^{2} = (1 + 4)^{2} + (-4 - 0)^{2} **

= 25 + 16 = 41,

BC^{2} = (5 - 1)^{2} + (1 + 4)^{2} = 4^{2} + 5^{2}

= 16 + 25 = 41

AC^{2} = (5 + 4)^{2} + (1 - 0)^{2}

= 81 + 1 = 82

AB = BC and AB^{2} = BC^{2} = AC^{2}

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, x _{1} = 2, x_{2} = -4, x_{3} = 5 and y_{1} = 8, y_{2} = 2, y_{3} = -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

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