Coordinate Geometry — Previous Year Questions (Class 10 Mathematics)
Coordinate Geometry uses algebraic methods to solve geometric problems. It covers distance formula, section formula, and slope of lines, enabling precise l
TL;DR: Coordinate Geometry uses algebraic methods to solve geometric problems. It covers distance formula, section formula, and slope of lines, enabling prec…
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Coordinate Geometry uses algebraic methods to solve geometric problems. It covers distance formula, section formula, and slope of lines, enabling precise l
Coordinate Geometry — Previous Year Questions with Solutions
Q (2023, 1 mark): Find the distance between points A(3, 4) and B(-1, 2).
Answer: Using distance formula: d = sqrt[(x2-x1)^2 + (y2-y1)^2]
d = sqrt[(-1-3)^2 + (2-4)^2]
d = sqrt[(-4)^2 + (-2)^2]
d = sqrt[16 + 4]
d = sqrt(20) = 2*sqrt(5)
Q (2022, 3 marks): Point P(4, 1) divides the line segment joining A(2, -2) and B(6, 4) in some ratio. Find the ratio.
Answer: Using section formula: if P divides AB in ratio m:n, then
P = ((m*x2 + n*x1)/(m+n), (m*y2 + n*y1)/(m+n))
4 = (m*6 + n*2)/(m+n) and 1 = (m*4 + n*(-2))/(m+n)
From first: 4(m+n) = 6m + 2n → 4m + 4n = 6m + 2n → 2n = 2m → m = n
So ratio is 1:1, meaning P is the midpoint.
Verify: midpoint = ((2+6)/2, (-2+4)/2) = (4, 1) ✓
Q (2023, 2 marks): Show that points A(1, 0), B(4, -5), and C(2, 3) are collinear.
Answer: For collinear points, slopes AB = BC
Slope of AB = (-5-0)/(4-1) = -5/3
Slope of BC = (3-(-5))/(2-4) = 8/(-2) = -4
-5/3 ≠ -4, so they are NOT collinear.
Alternatively, area of triangle = 0 for collinear points.
Area = (1/2)|1(-5-3) + 4(3-0) + 2(0-(-5))|
= (1/2)|-8 + 12 + 10| = (1/2)|14| = 7 ≠ 0
Points are NOT collinear.
Q (2021, 2 marks): Find the coordinates of the point that divides the line segment joining (1, 4) and (7, 10) internally in the ratio 2:1.
Answer: Using section formula for internal division in ratio 2:1:
Point = ((2*7 + 1*1)/(2+1), (2*10 + 1*4)/(2+1))
= ((14 + 1)/3, (20 + 4)/3)
= (15/3, 24/3)
= (5, 8)
Q (2022, 3 marks): If A(-2, -2), B(2, 2), C(1, 5) are vertices of a triangle, find its area.
Answer: Area = (1/2)|x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|
= (1/2)|(-2)(2-5) + 2(5-(-2)) + 1((-2)-2)|
= (1/2)|(-2)(-3) + 2(7) + 1(-4)|
= (1/2)|6 + 14 - 4|
= (1/2)|16|
= 8 square units
Q (2023, 1 mark): Find the slope of the line passing through points (-1, 2) and (3, -4).
Answer: Slope m = (y2-y1)/(x2-x1)
m = (-4-2)/(3-(-1))
m = -6/4
m = -3/2
Frequently Asked Questions
What is the distance formula?
The distance between points (x1, y1) and (x2, y2) is d = sqrt[(x2-x1)^2 + (y2-y1)^2]. It comes from the Pythagorean theorem.
How does the section formula work?
If point P divides line AB in ratio m:n, then P = ((m*x2+n*x1)/(m+n), (m*y2+n*y1)/(m+n)). When m=n, P is the midpoint.
More Class 10 Mathematics PYQs
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