Chapter 5: Coordinate Geometry — Online MCQ Test
MATHS · CLASS 10th · Tamil Nadu State Board
Practice Chapter 5: Coordinate Geometry with a free chapter-wise online MCQ test.
This chapter covers: Cartesian plane Coordinates Distance formula Section formula Area of triangle Area of quadrilateral Slope Intercepts Equation of straight line Parallel lines Perpendicular lines.
AI-generated questions from basic to board-exam level, with instant results and explanations.
Chapter 5: Coordinate Geometry — Important Questions & Answers
What are the coordinates of the origin in the Cartesian plane?
- A. (0, 0)
- B. (1, 0)
- C. (0, 1)
- D. (1, 1)
Answer: A. (0, 0)
The origin is the point where the x-axis and y-axis intersect. Hence its coordinates are (0, 0).
The origin is the point where the x-axis and y-axis intersect. Hence its coordinates are (0, 0).
The distance between two points (x1, y1) and (x2, y2) is given by ______.
- A. sqrt((x2 - x1)^2 + (y2 - y1)^2)
- B. (x2 - x1) + (y2 - y1)
- C. sqrt((x2 + x1)^2 + (y2 + y1)^2)
- D. (x1x2 + y1y2)
Answer: A. sqrt((x2 - x1)^2 + (y2 - y1)^2)
The distance formula is derived from Pythagoras theorem. It is sqrt((x2 - x1)^2 + (y2 - y1)^2).
The distance formula is derived from Pythagoras theorem. It is sqrt((x2 - x1)^2 + (y2 - y1)^2).
The midpoint of the line segment joining (x1, y1) and (x2, y2) is ______.
- A. ((x1 + x2)/2, (y1 + y2)/2)
- B. ((x1 - x2)/2, (y1 - y2)/2)
- C. (x1 + x2, y1 + y2)
- D. (x2 - x1, y2 - y1)
Answer: A. ((x1 + x2)/2, (y1 + y2)/2)
The midpoint is found by taking the average of the x-coordinates and the average of the y-coordinates.
The midpoint is found by taking the average of the x-coordinates and the average of the y-coordinates.
Which of the following points lies on the x-axis?
- A. (5, 0)
- B. (0, 5)
- C. (5, 5)
- D. (-5, 2)
Answer: A. (5, 0)
A point on the x-axis has y-coordinate equal to 0. Therefore, (5, 0) lies on the x-axis.
A point on the x-axis has y-coordinate equal to 0. Therefore, (5, 0) lies on the x-axis.
Find the distance between the points (3, 4) and (-1, 1).
- A. 5
- B. 4
- C. sqrt(7)
- D. 25
Answer: A. 5
Distance = sqrt((-1 - 3)^2 + (1 - 4)^2) = sqrt(16 + 9) = 5.
Distance = sqrt((-1 - 3)^2 + (1 - 4)^2) = sqrt(16 + 9) = 5.
Find the midpoint of the line segment joining (-2, 5) and (4, -1).
- A. (1, 2)
- B. (2, 1)
- C. (-1, 2)
- D. (1, -2)
Answer: A. (1, 2)
Midpoint = ((-2 + 4)/2, (5 + (-1))/2) = (1, 2).
Midpoint = ((-2 + 4)/2, (5 + (-1))/2) = (1, 2).
If the distance between (k, 3) and (4, -1) is 5 units, find the possible values of k.
- A. 1 or 7
- B. -1 or 7
- C. 1 or -7
- D. 4 or 5
Answer: A. 1 or 7
Using distance formula, (k - 4)^2 + (3 + 1)^2 = 25. Thus (k - 4)^2 = 9, so k = 1 or 7.
Using distance formula, (k - 4)^2 + (3 + 1)^2 = 25. Thus (k - 4)^2 = 9, so k = 1 or 7.
The point P(4, 5) divides the line segment joining A(1, 2) and B(7, 8). Find the ratio AP:PB.
- A. 1:1
- B. 1:2
- C. 2:1
- D. 3:2
Answer: A. 1:1
The midpoint of A(1, 2) and B(7, 8) is ((1+7)/2, (2+8)/2) = (4, 5). Hence P divides AB in the ratio 1:1.
The midpoint of A(1, 2) and B(7, 8) is ((1+7)/2, (2+8)/2) = (4, 5). Hence P divides AB in the ratio 1:1.
Find the equation of the line whose intercepts on the coordinate axes are equal and which passes through (4, -2).
- A. x + y = 2
- B. x - y = 2
- C. x + y = 6
- D. 2x + y = 6
Answer: A. x + y = 2
If the intercepts are equal, the equation is x/a + y/a = 1, or x + y = a. Since it passes through (4, -2), a = 4 - 2 = 2.
If the intercepts are equal, the equation is x/a + y/a = 1, or x + y = a. Since it passes through (4, -2), a = 4 - 2 = 2.
The point R divides the line segment joining P(-2, 5) and Q(4, -1) externally in the ratio 2:1. Find R.
- A. (10, -7)
- B. (2, 1)
- C. (6, -3)
- D. (-10, 7)
Answer: A. (10, -7)
Using external section formula, R = ((2(4) - 1(-2))/(2 - 1), (2(-1) - 1(5))/(2 - 1)) = (10, -7).
Using external section formula, R = ((2(4) - 1(-2))/(2 - 1), (2(-1) - 1(5))/(2 - 1)) = (10, -7).