Solved Questions: Coordinate Geometry | Quantitative Aptitude for SSC CGL PDF Download

Coordinate Geometry

Coordinate geometry is a mathematical field that facilitates the representation of geometric shapes on a two-dimensional plane and the understanding of their properties. To establish a foundational understanding of coordinate geometry, we will delve into the concepts of the coordinate plane and the coordinates of a point.

Co-ordinate Geometry Rules

• The point where the x and y axes intersect is termed the origin, with both x and y coordinates being 0 at this point.
• Positive values are found on the right side of the x-axis, while negative values are located on the left side.
• Positive values occur above the y-axis, while negative values occur below it.
• A point on the plane can be pinpointed by a pair of two numbers. The first value corresponds to the x-axis, and the second value corresponds to the y-axis, determining the combined position on the plane.

Example 1: Find the equation of straight line passing through (2, 3) and perpendicular to the line 3x + 2y + 4 = 0
(a) y = 5/3x- 2
(b) 3Y = 2x+5
(c) 3Y = 5x-2
(d) None of these
Ans: (b)
The given line is 3x + 2y + 4 = 0 or y = -3x / 2 – 2
Any line perpendicular to it will have slope = 2 / 3

3y – 9 = 2x – 4
3y – 2x – 5 = 0.

Example 2: Find the coordinate of the point which will divide the line joining the point (2,4) and (7,9) internally in the ratio 1:2?
(a) (5/3 , 1/3)
(b) (3/8 , 3/11)
(c) (8/3 , 11/3)
(d) (11/3 , 17/3)
Ans: (d)
The internal division will use the formula

So, the point becomes (11/3, 17/3).

CO-ordinate Geometry Questions and Answers

Q1: (0, 0, 0) (a, 0, 0), (0, b, 0) and (0, 0, c) are four distinct points. What are the coordinates of the point which is equidistant from the four points?
(a) ((a+b+c)/3, (a+b+c)/3, (a+b+c)/3)
(b) (a, b, c)
(c) (a/3, b/3, c/3)
(d) (a/2, b/2, c/2)
Ans: (d)

Q2: If the centroid of a triangle formed by (7, x), (y, –6), and (9, 10) is (6, 3), then the values of x and y are respectively.
(a) 5,2
(b) 2,5
(c) 1,0
(d) 0,0
Ans: (a)

y = 2 and x = 5

Q3: The co-ordinates of incentre of ∆ ABC with vertices A(0, 6), B(8, 12), and C(8, 0) is.
(a) (5, 6)
(b) (–4, 3)
(c) (8, 11)
(d) (16/3,0)
Ans: (a)

Incenter is

Q4: If t₁ ≠ t₂ and the points A (a, 0), B (at1², 2at₁) and C (at2², 2at²) are collinear, then t₁ t₂ is equal to
(a) 1
(b) -1
(c) 2
(d) -2
Ans: (b)

Q5: The vertices of a triangle ABC are A (2, 3, 1), B (–2, 2, 0), and C(0, 1, –1). What is the magnitude of the line joining mid points of the sides AC and BC?
(a) 1/√2 unit
(b) 1 unit
(c) 3/√2 unit
(d) 2 unit
Ans: (c)
Mid Point of A and C

Mid Point of B and C

Magnitude