Coordinate geometry is a mathematical field that facilitates the representation of geometric shapes on a twodimensional 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.
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 = 5x2
(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).
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 coordinates 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 t_{1} ≠ t_{2} and the points A (a, 0), B (at1^{2}, 2at_{1}) and C (at2^{2}, 2at^{2}) are collinear, then t_{1} t_{2} 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
314 videos170 docs185 tests

1. What is coordinate geometry? 
2. How do you find the distance between two points in coordinate geometry? 
3. What is the midpoint formula in coordinate geometry? 
4. How do you find the slope of a line in coordinate geometry? 
5. What is the equation of a line in coordinate geometry? 
314 videos170 docs185 tests


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