Coordinate Geometry — Previous Year Questions (Class 9 Mathematics)
Coordinate geometry connects algebra and geometry using the Cartesian plane. Master distance, midpoint, and area calculations using coordinates.
TL;DR: Coordinate geometry connects algebra and geometry using the Cartesian plane. Master distance, midpoint, and area calculations using coordinates.
Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated
Coordinate geometry connects algebra and geometry using the Cartesian plane. Master distance, midpoint, and area calculations using coordinates.
Coordinate Geometry — Previous Year Questions with Solutions
Q (2023, 2 marks): Find the distance between points A(2, 3) and B(5, 7).
Answer: Using distance formula: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
d = sqrt((5 - 2)^2 + (7 - 3)^2)
d = sqrt(3^2 + 4^2)
d = sqrt(9 + 16)
d = sqrt(25) = 5 units
Q (2022, 2 marks): Find the midpoint of the line segment joining A(-3, 4) and B(5, -2).
Answer: Using midpoint formula: M = ((x1 + x2)/2, (y1 + y2)/2)
M = ((-3 + 5)/2, (4 + (-2))/2)
M = (2/2, 2/2)
M = (1, 1)
Q (2023, 3 marks): Show that the points A(2, 1), B(5, 2), and C(8, 3) are collinear.
Answer: Points are collinear if area of triangle = 0
Using area formula: Area = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Area = (1/2)|2(2 - 3) + 5(3 - 1) + 8(1 - 2)|
Area = (1/2)|2(-1) + 5(2) + 8(-1)|
Area = (1/2)|-2 + 10 - 8|
Area = (1/2)|0| = 0
Since area = 0, points are collinear
Q (2021, 2 marks): Find the area of triangle with vertices A(0, 0), B(4, 0), and C(0, 3).
Answer: Using area formula: Area = (1/2)|x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Area = (1/2)|0(0 - 3) + 4(3 - 0) + 0(0 - 0)|
Area = (1/2)|0 + 12 + 0|
Area = (1/2) × 12 = 6 square units
Alternatively (right triangle): Area = (1/2) × base × height = (1/2) × 4 × 3 = 6
Q (2022, 3 marks): Verify whether the quadrilateral with vertices A(0, 0), B(4, 0), C(4, 3), D(0, 3) is a square or rectangle.
Answer: Calculate side lengths:
AB = sqrt((4-0)^2 + (0-0)^2) = 4
BC = sqrt((4-4)^2 + (3-0)^2) = 3
CD = sqrt((0-4)^2 + (3-3)^2) = 4
DA = sqrt((0-0)^2 + (0-3)^2) = 3
Opposite sides equal: AB = CD = 4, BC = DA = 3
Diagonals:
AC = sqrt((4-0)^2 + (3-0)^2) = sqrt(16 + 9) = 5
BD = sqrt((0-4)^2 + (3-0)^2) = sqrt(16 + 9) = 5
Diagonals equal, adjacent sides unequal
Therefore, ABCD is a rectangle
Q (2023, 3 marks): If P(x, 2) is equidistant from Q(3, 1) and R(0, 5), find the value of x.
Answer: Since P is equidistant from Q and R: PQ = PR
sqrt((x - 3)^2 + (2 - 1)^2) = sqrt((x - 0)^2 + (2 - 5)^2)
sqrt((x - 3)^2 + 1) = sqrt(x^2 + 9)
Square both sides:
(x - 3)^2 + 1 = x^2 + 9
x^2 - 6x + 9 + 1 = x^2 + 9
-6x + 10 = 9
-6x = -1
x = 1/6
Frequently Asked Questions
What is the distance formula and when is it used?
Distance formula d = sqrt((x2 - x1)^2 + (y2 - y1)^2) finds the straight-line distance between two points on a coordinate plane. It's derived from the Pythagorean theorem.
How do you prove three points are collinear using coordinate geometry?
Three points are collinear if the area of the triangle formed by them is zero. Use the area formula with their coordinates; if area = 0, they are collinear.
More Class 9 Mathematics PYQs
🤖 Stuck on any of these? Ask Syllab's free AI Tutor to explain step by step →