Solved Questions: Coordinate Geometry

# 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

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## FAQs on Solved Questions: Coordinate Geometry - Quantitative Aptitude for SSC CGL

 1. What is coordinate geometry?
Ans. Coordinate geometry is a branch of mathematics that deals with the study of geometric shapes using coordinate systems. It involves the use of algebraic equations to represent points, lines, curves, and other geometric objects on a coordinate plane.
 2. How do you find the distance between two points in coordinate geometry?
Ans. To find the distance between two points in coordinate geometry, you can use the distance formula. The distance between two points (x1, y1) and (x2, y2) is given by the formula: Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
 3. What is the midpoint formula in coordinate geometry?
Ans. The midpoint formula in coordinate geometry is used to find the coordinates of the point that lies exactly halfway between two given points. The midpoint of two points (x1, y1) and (x2, y2) is given by the formula: Midpoint = [(x1 + x2)/2, (y1 + y2)/2]
 4. How do you find the slope of a line in coordinate geometry?
Ans. The slope of a line in coordinate geometry is a measure of its steepness. It indicates how much the line rises or falls for a given horizontal distance. The slope of a line passing through two points (x1, y1) and (x2, y2) is given by the formula: Slope = (y2 - y1)/(x2 - x1)
 5. What is the equation of a line in coordinate geometry?
Ans. The equation of a line in coordinate geometry represents the relationship between the x and y coordinates of its points. It can be expressed in different forms, such as slope-intercept form (y = mx + b), point-slope form (y - y1 = m(x - x1)), or standard form (Ax + By = C), where m represents the slope of the line and (x1, y1) represents a point on the line.

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