Coordinate Geometry

If x is a positive integer such that the distance between points P(x, 2) and Q(3, -6) is 10 units, then x is:
1. 3
2. - 3
3. 9
4. - 9
The distance between the points $(\cos θ, \sin θ)$ and $(\sin θ, - \cos θ)$ is:
1. $\sqrt{3}$
2. $\sqrt{2}$
3. 2
4. 1
A line segment is of length 10 units. If the coordinates of its one end are (2, -3) and the abscissa of the other end is 10, then its ordinate is:
1. (9, 6)
2. (3, - 9)
3. (- 3, 9)
4. (9, - 6)
The perimeter of the triangle formed by the points (0, 0), (1, 0) and (0, 1) is:
1. $1 \pm \sqrt{2}$
2. $\sqrt{2} + 1$
3. 3
4. $\sqrt{2} + 2$
If A(2, 2), B(- 4, - 4) and C(5, - 8) are the vertices of a triangle, then the length of the median through vertex C is:
1. $\sqrt{65}$
2. $\sqrt{117}$
3. $\sqrt{85}$
4. $\sqrt{113}$
If points (a, 0), (0, b) and (1, 1) are collinear, then $\frac{1}{a} + \frac{1}{b}$ :
1. 1
2. 2
3. 0
4. - 1
The ratio in which (4, 5) divides the join of (2, 3) and (7, 8) is:
1. - 2 : 3
2. - 3 : 2
3. 3 : 2
4. 2 : 3
If the centriod of the triangle formed by the points (3, - 5), (- 7, 4) and (10, - k) is at the point (k, - 1), then k is:
1. 3
2. 1
3. 2
4. 4
If (- 2, 1) is the centroid of the triangle having its vertices at (x, 0), (5, - 2), (- 8, y), then x, y satisfy the equation:
1. 3x + 8y = 0
2. 3x - 8y = 0
3. 8x + 3y = 0
4. 8x = 3y
The area of $∆ A B C$ (in square units) is:
1. 7.5
2. 10
3. 15
4. 2.5
The point which divides the joint of ( 1, 2 ) and ( 3,4 ) externally in the ratio 1 : 1 .
1. Cannot be found
2. Lies in first quadrant
3. Lies in second quadrant
4. Lies in third quadrant
The distance of the point ( x, y ) from the origin is:
1. x + y
2. x
3. y
4. $\sqrt{x^{2} + y^{2}}$
The distance of the point ( x , y ) from Y axis is:
1. None of these
2. $|x|$
3. $|y|$
4. y
Slope of a line is not defined if the line is:
1. Parallel to X axis
2. Parallel to Y axis
3. Parallel to the line x + y
4. Parallel to the line x - y
The line through the points (a, b) and (- a, - b) passes through the point:
1. ( 3a, - 2b )
2. $(a^{2}, a b)$
3. (1, 1)
4. None of these
The distance between the lines 5x – 12y + 65 = 0 and 5x – 12y – 39 = 0:
1. 8
2. None of these
3. - 2
4. 2
The equation $y - y_{1} = m (x - x_{1}), m \in R$ , represents all lines through the point $(x_{1}, y_{1})$ except the line:
1. Parallel to X axis
2. Parallel to the line x – y = 0
3. Parallel to Y axis
4. None of these
Slope of any line parallel to X axis is:
1. - 1
2. 1
3. None of these
4. 0
The distance between the parallel lines 3x + 4y + 13 = 0 and 3x + 4y – 13 = 0 is:
1. $\frac{26}{3}$
2. $\frac{26}{5}$
3. 26
4. $\frac{26}{4}$
The straight lines x + y = 0 , 3x - y – 4 = 0 , x + 3y – 4 = 0 form a triangle which is:
1. Right angled
2. Isosceles
3. Equilateral
4. None of these
The lines 2x – 3y = 5 and 6x – 9y – 7 = 0 are:
1. Parallel
2. Coincident
3. Perpendicular
4. None of these
The area of a triangle with vertices at (- 4, - 1), (1, 2) and (4, - 3) is:
1. 17
2. 16
3. 15
4. None of these
The cemtroid of a triangle is (2, 7) and two of its vertices are (4, 8) and (- 2, 6). The third vertex is:
1. (0, 0)
2. (4, 7)
3. (7, 4)
4. (7, 7)
The line segment joining the points (1, 2) and (- 2, 1) is divided by the line 3x + 4y = 7 in the ratio:
1. 3 : 4
2. 4 : 3
3. 9 : 4
4. 4 : 9
A(6, 3), B(- 3, 5) and C(4, - 2) and D(x, 3x) are four points. If $∆ D B C : ∆ A B C = 1 : 2$ , then x is equal to:
1. $\frac{11}{8}$
2. $\frac{8}{11}$
3. 3
4. None of these
The equation of the line passing through (1, 5) and perpendicular to the line 3x - 5y + 7 = 0 is:
1. 5x + 3y - 20 = 0
2. 3x - 5y + 7 = 0
3. 3x - 5y + 6 = 0
4. 5x + 3y + 7 = 0
The angle between the lines 2x - y + 3 = 0 and x + 2y + 3 = 0:
1. $90 °$
2. $60 °$
3. $45 °$
4. $30 °$
Find the value of ‘k’, if the point (0, 2) is equidistant from the points (3, k) and (k, 5):
1. 2
2. 1
3. - 1
4. 0
If the point P(2, 4) lies on a circle, whose centre is C(5, 8), then the radius of the circle is:
1. 8 units
2. 5 units
3. 4 units
4. 25 units
The vertices of a square are (0, – 1), (2, 1), (0, 3) and (– 2, 1). The side of the square is:
1. 2 units
2. $2 \sqrt{3}$ units
3. $2 \sqrt{2}$
4. $\sqrt{2}$ units

Coordinate Geometry

Quiz