Summary:Coordinate Geometry

Q.

The equation of the line passing through $(4,-6)$and makes an angle $45°$with positive$x$ axis, is

1. $x-y-10=0$

2. $x-2y-16=0$

3. $x-3y-22=0$

4. None of these

Q. The orthocentre of the triangle with vertices
$(2,\frac{\sqrt{3}-1}{2}),(\frac{1}{2},-\frac{1}{2})and(2,-\frac{1}{2})$ is

1. $(\frac{3}{2},\frac{\sqrt{3}-3}{6})$
2. $(2,-\frac{1}{2})$
3. $(\frac{5}{4},\frac{\sqrt{3}-2}{4})$
4. $(\frac{1}{2},-\frac{1}{2})$

Q.

The point P(1, 2) divides the line joining the points A(-2, 1) and B(7, 4) in the ratio 2 : 1

1. True

2. False

Q. Find the equation of the line which cuts off an intercept 4 on negative direction of x-axis and an intercept of 2 on positive direction of y-axis.

1. x - 2y + 4 = 0
2. x + 2y - 4 = 0
3. 2x - y + 4 = 0
4. 2x + y - 4 = 0

Q. Find the equation of a line passing through (3, -4) having slope $\frac{1}{2}.$

1. x - 2y - 11 = 0
2. x - 2y - 8 = 0
3. 2x - y - 11 = 0
4. None of These

Q. Question 20
Find the ratio in which the line 2x+3y = 5 = 0 divides the line segment joining the points (8, -9) and (2, 1). Also, find the coordinates of the point of division.

Q. a) Find the ratio in which the point P (-1, a) divides the joining of points A(-5, 4) and B (3, -2). Hence, find a.

b)
The line joining the points A(4, -5) and B (4, 5) is divided by the point P, such that AP: PB = 2 : 3. Find the coordinates of point P.

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Q. Find the equation of the median through the vertex A of $\Delta ABC$ whose vertices are A(2, 5), B(-4, 9) and C(-2, -1).

1. x - 5y + 23 = 0
2. x + 5y + 23 = 0
3. x + 5y - 23 = 0
4. x - 5y - 23 = 0

Q.

If $f\left(\alpha \right)=x\cos \alpha +y\sin \alpha -p\left(\alpha \right)$, then the lines $f\left(\alpha \right)=0$ and $f\left(\beta \right)=0$ are perpendicular to each other, if

1. $\alpha =\beta$

2. $\alpha +\beta =\frac{\pi }{2}$

3. $|\alpha -\beta |=\frac{\pi }{2}$

4. $\alpha \pm \beta =\frac{\pi }{2}$

Q. Find the value of x for which the area of the triangle with vertices at (-1, -4), (x, 1) and (x, -4) is 12¹/₂ sq. units.

1. 2
2. 4
3. -3
4. -6

Q. Find the slope of a line whose inclination to the positive direction of x-axis in anticlockwise direction is 30°.

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

Q. a) In what ratio, the line segment joining (-3, -1) and (-8, -9) is divided at the point (-5, 3)?

b) For what value of $a$, the points (a, 1), (1, -1) and (11, 4) are collinear?

[6 MARKS]

Q. If a line passes through (1, 1) and (2, 2) then find the angle made by the line with x-axis.

1. 30°
2. 45°
3. 60°
4. 90

Q. Question 6
The perimeter of a triangle with vetices (0, 4), (0, 0) and (3, 0) is:
(A) 5
(B) 12
(C) 11
(D) $7+\sqrt{5}$

Q.

Ratio in which line $2x+3y-5=0$ divides the line segment joining the points A(8 , -9) and B(2 , 1) is .

1. 8 : 1
2. 7 : 1
3. 8 : 3

Q. If (1, 2), (4, y), (x, 6) and (3, 5) are the vertices of a parallelogram taken in order, find x and y.

1. (2, 5)
2. (6, 3)
3. (2, 3)
4. (4, 3)

Q. The slope of a line perpendicular to the line $3x=4y+11$ is

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

Q. Find the equation of the line whose perpendiculat distance from origin is 3 units and the angle which the normal makes with the positive direction of x-axis is 30°.

1. $\sqrt{3}x+y=6$
2. $x+\sqrt{3}y=6$
3. $\sqrt{3}x+y=3$
4. None of These

Q. The coordinates of two points A and B are (3, 4) and (5, -2) respectively. If P is any point such that PA = PB and area of $\Delta PAB=10$ square units, then find the coordinates of point P.

1. (1, 0) or (7, 2)
2. (0, 1) or (2, 7)
3. (1, 0) or (2, 7)
4. (0, 1) or (7, 2)

Q.

The midpoint of the line joining the points (0, 0) and (-8, -6) is

1. (-4, -3)

2. (2, -4)

3. (4, 2)

4. (4, 3)

Q.

If $|z_1|=|z_2|=|z_3|=1$ and $z_1+z_2+z_3=0$
then area of the triangle whose vertices are $z_1,z_2,z_3$ is

1. 1

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

3. $\frac{\sqrt{3}}{4}$

4. 2

Q. A(4, 3) and B(6, 4) are the two given points. Find the slope of a line which is perpendicular to AB.

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

Q. What is the value of y so that the line passing through (3, y) and (2, 7) is parallel to the line passing through (-1, 4) and (0, 6)?

1. 9
2. -9
3. $\frac{1}{9}$
4. $-\frac{1}{9}$

Q.

The midpoint of the line joining the points (1, 2) and (5, 6) is

1. They Are Always Equal

2. They Are Always Positive

3. They Are Always Negative

4. They Are Always 0

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

Q. Assertion: Points A(6, 4), B(-4, -6) and C(4, 6) are such that AB =$\sqrt{200}$, BC= $\sqrt{208}$, AC= $\sqrt{8}$, Since AB+BC>AC, points A, B and C from a triangle.

Reason: If $B{C}^2=A{B}^2+A{C}^2$, then $\Delta ABC$ is a right triangle, right angled at A.

1. If assertion is false but reason is true.
2. If both assertion and reason are true and reason is te correct explanation of assertion
3. If both assertion and reason are true but reason is not the correct explanation of assertion.
4. If assertion is true but reason is false.

Q. Find the value of x and match the following.

1. -1
2. 7
3. 2

Q. Find the area and match the pair.

1. 47.5 square units
2. 72 square units
3. 10.5 square units

Q.

If the centroid of a triangle is (1, 4) and two of its vertices are (4, -3) and (-9, 7), then the area of the triangle is

1. 183 sq. units

2. $\frac{183}{2}sq.units.$

3. 366 sq. units

4. $\frac{183}{4}sq.units.$

Q.

Determine the ratio in which the line $2x+y-4=0$ divides the line segment joining the points A (2, -2) and B (3, 7).

1. 2 : 9

2. 9 : 2

3. 9 : 1

4. 1 : 9