Coordinate Geometry

Which statement best summarizes the chapter "Coordinate Geometry"?

1. Coordinate Geometry studies only straight lines.
2. Coordinate Geometry introduces formulas for distance, midpoint, and section of a line segment, allowing geometric problems to be solved using algebraic methods.
3. Coordinate Geometry deals only with circles.
4. Coordinate Geometry has no practical applications.

The section formula is mainly used to:

1. Find area only
2. Find the point dividing a line segment in a given ratio
3. Measure angles
4. Draw circles

Which formula gives the distance from the origin to the point (x, y)?

1. square root of (x+y)
2. square root of (x squared + y squared)
3. x+y
4. x-y

Which quadrant contains the point (-4, -7)?

1. First Quadrant
2. Second Quadrant
3. Third Quadrant
4. Fourth Quadrant

A point divides the line joining (2,2) and (8,8) internally in the ratio 1:1. The point is:

1. (4,4)
2. (5,5)
3. (6,6)
4. (7,7)

The midpoint of a line segment divides it into:

1. Three equal parts
2. Two equal parts
3. Four equal parts
4. Unequal parts

Find the distance between (-2, 1) and (4, 1).

1. 4 units
2. 5 units
3. 6 units
4. 7 units

Which theorem is the basis of the distance formula?

1. Midpoint Theorem
2. Basic Proportionality Theorem
3. Pythagoras Theorem
4. Angle Bisector Theorem

What is the distance between (0, 0) and (3, 4)?

1. 4 units
2. 5 units
3. 6 units
4. 7 units

Find the midpoint of the points (2, -4) and (8, 6).

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

Which formula is used to divide a line segment internally in the ratio m:n?

1. Midpoint Formula
2. Section Formula
3. Distance Formula
4. Area Formula

The midpoint of the line segment joining (4, 6) and (8, 10) is:

1. (5, 7)
2. (6, 8)
3. (7, 9)
4. (8, 8)

What is the distance between the points (2, 3) and (6, 6)?

1. 3 units
2. 4 units
3. 5 units
4. 6 units

The distance between (a, 0) and (0, a) is √50. Find a.

1. 3 or −3
2. 4 or −4
3. 5 or −5
4. 6 or −6

Find the point on the y-axis equidistant from (3, 2) and (−1, 4).

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

The points (1, 2), (4, 6), (7, 10) lie on:

1. a circle
2. a straight line
3. a triangle
4. none

A point P divides the segment joining (6, −2) and (−3, 4) in the ratio 2 : 1. Find the x-coordinate of P.

1. 2
2. 1
3. 0
4. −1

Find the coordinates of the point on the x-axis which is equidistant from (2, 3) and (−2, 5).

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

If the distance between the points (3, k) and (7, 6) is 5 units, find the value of k.

1. 1 or 11
2. 2 or 10
3. 3 or 9
4. 4 or 8

Find the distance between the points (−2, −3) and (4, 5).

1. 8 units
2. 10 units
3. 12 units
4. 14 units

The point (4, 4) divides the line segment joining A(1, 2) and B(x, 8) internally in the ratio 1 : 2. Find the value of x.

1. 8
2. 9
3. 10
4. 11

The midpoint of the line segment joining A(3, 7) and B(x, 11) is (7, 9). Find the value of x.

1. 9
2. 10
3. 11
4. 12

A point P is equidistant from the points A(4, 2) and B(4, 10). Which of the following could be the coordinates of P?

1. (6, 6)
2. (6, 8)
3. (2, 5)
4. (8, 4)

The distance between the points A(2, 3) and B(x, 15) is 13 units. If x > 2, then the value of x is:

1. 5
2. 7
3. 8
4. 10

Find the coordinates of the midpoint of the line segment joining the points (−7, 9) and (5, −3).

1. (−2, 2)
2. (−1, 3)
3. (1, 2)
4. (−3, 4)

Point P divides the line segment joining A(2, 5) and B(8, 17) internally in the ratio 1 : 2. What are the coordinates of P?

1. (4, 9)
2. (5, 10)
3. (6, 11)
4. (4, 11)

The coordinates of points A and B are (−4, 3) and (6, 3), respectively. Find the distance between A and B.

1. 8 units
2. 9 units
3. 10 units
4. 12 units

Area of triangle enclosed between coordinate axes with vertices (6,0) and (0,11)

1. 4 sq units
2. 5 sq units
3. 10 sq units
4. 33 sq units

Segment (5,1) and (–7,–1) divided by X-axis in ratio

1. 1:6
2. 6:2
3. 2:6
4. 1:1

Two vertices (–1,4),(5,2); medians intersect at (0,–3). Third vertex is

1. (4,15)
2. (3,15)
3. (–4,15)
4. (–4,–15)

A(–1,2),B(4,1),C(7,6) are vertices of parallelogram ABCD. Fourth vertex D is

1. (7,2)
2. (–2,7)
3. (7,–2)
4. (2,7)

Centre of circle through (1,2),(3,–4),(5,–6)

1. (2,11)
2. (11,2)
3. (11,–2)
4. (–2,11)

If distance between (p,–7) and (9,–7) is 15, then p is

1. –3 or 7
2. –7 or 3
3. –3 or –7
4. –6 or 24

Perimeter of triangle formed by (0,0),(1,0),(0,1)

1. option a
2. option b
3. 3
4. option d

If distance between (1,p) and (p,5) is 5, then p =

1. ±4, 0
2. 4
3. 4
4. 0

Line 3x+y=9 divides segment (1,3) and (2,7). Ratio is

1. 1:2
2. 2:1
3. 3:8
4. 3:2

Distance between two fractional trigonometric points (doc Q31)

1. option a
2. option b
3. option c
4. option d

Three points form a triangle; what type? (doc Q30)

1. Right triangle
2. Equilateral triangle
3. Isosceles triangle
4. Scalene triangle

Distance between two fractional points (doc Q29)

1. option a
2. option b
3. option c
4. option d

Vertices of right triangle at A; find value of a

1. 2
2. 1
3. 3
4. 4

Area of rhombus with vertices (3,0),(4,5),(–1,4),(–2,–1)

1. 24 sq units
2. 30 sq units
3. 28 sq units
4. 25 sq units

Vertices of triangle and centroid given; find a and b (doc Q26)

1. option a
2. option b
3. option c
4. option d

Ratio in which x-axis divides fractional segment (doc Q25)

1. option a
2. option b
3. option c
4. option d

Point dividing the line segment joining two fractional points (doc Q24)

1. option a
2. option b
3. option c
4. option d

Vertices A, B, C given. Length of median through A (doc Q23)

1. √130 units
2. √261 units
3. √244 units
4. √200 units

If point divides AB in 3:4, A given, find B (doc Q22)

1. option a
2. option b
3. option c
4. option d

Centre of circle with diameter endpoints given (doc Q21)

1. option a
2. option b
3. option c
4. option d

Midpoint of line joining fractional points is given; find p and q (doc Q20)

1. option a
2. option b
3. option c
4. option d

Values of x such that PQ=QR with given coordinates (doc Q19)

1. option a
2. option b
3. option c
4. option d

Midpoint of line joining two fractional points (doc Q18)

1. option a
2. option b
3. option c
4. option d

Centroid of triangle with given fractional vertices (doc Q17)

1. option a
2. option b
3. option c
4. option d

Point on y-axis equidistant from two fractional points (doc Q16)

1. option a
2. option b
3. option c
4. option d

Point on y-axis equidistant from (2,3) and (–4,1)

1. (0,4)
2. (0,–1)
3. (0,0)
4. (0,5)

Centroid of triangle with vertices (4,–8),(–9,7),(8,13) is

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

Distance between two points (given as 10 units), value of m is

1. m=2
2. m=4
3. m=6 or –2
4. m=–6 or 2

Distance between two points (given in doc, answer=5)

1. 4
2. 5
3. 6
4. 4

If (2,2p+2) is midpoint of (3p,4) and (–2,2q), then p and q are

1. 2, 4
2. 3, 6
3. 7, 9
4. 8, 10

If (2,3),(4,a),(6,–3) are collinear, the value of k=

1. –3/7
2. 3/7
3. –7/3
4. 7/3

Area of triangle with vertices A(2,0), B(–1,0), C(0,0) — typical vertex question — is

1. 32 sq units
2. 34 sq units
3. 36 sq units
4. 40 sq units

Point dividing (1,3) and (–2,7) in ratio 3:4 internally

1. (1,3)
2. (3/7,33/7)
3. (–5/7,33/7)
4. (3/7,–33/7)

Centroid of triangle is (2,3/7). Two vertices are (3,1) and (1,2). Third vertex is

1. (2,–1/7)
2. (2,0)
3. (0,2)
4. (–1,2)

Value of k if P(–1,2) is equidistant from A(2,k) and B(k,–1)

1. k=3/2
2. k=1/2
3. k=5/2
4. k=7/2

The ratio in which x-axis divides internally (2,–3) and (3,5) is

1. 1:2
2. 2:3
3. 3:5
4. 5:7

If (–2,–5),(2,–2),(8,a) are collinear, the value of a is

1. 5/2
2. 1/2
3. 3/2
4. 7/2

The line joining (2,–3) and (5,6) divided by x-axis and y-axis in ratios

1. 1:2 internally, 2:5 externally
2. 1:2 internally, 2:5 internally
3. 1:2 externally, 2:5 internally
4. 1:2 externally, 2:5 externally

Distance between (a·sinα, –b·cosα) and (–a·cosα, b·sinα) is

1. √(a²+b²)
2. √(2(a²+b²))
3. √(a²–b²)
4. √(2(a²–b²))

The line joining (–3,2) and (4,6) is cut by x-axis in the ratio

1. 2:3 internally
2. 1:2 externally
3. 1:3 externally
4. 3:2 internally