Coordinate Geometry Quiz - CBSE Class 10 Mathematics
Free practice quiz: Coordinate Geometry (CBSE Class 10 Mathematics). 18 multiple-choice questions with answers and explanations. Play online, no sign-up needed.
This CBSE Class 10 Mathematics practice quiz has 18 multiple-choice questions on Coordinate Geometry, and 18 of them come with an explanation. Try the 5 sample questions below (tap an option to check yourself), then play the full quiz online. No sign-up needed.
Start quiz: 18 questions, freeAbout this topic
A point on the Cartesian plane is written as (x, y). We use formulas to find the distance between points, the point dividing a segment in a ratio, and the area of a triangle. These help prove shapes like parallelograms and check collinearity.
- Point (x, y): x is the signed distance from the y-axis, y from the x-axis. Actual distances are |x| and |y|.
- Quadrants: I (+ , +), II (−, +), III (−,−), IV (+ ,−).
- Origin is (0,0). Points on x-axis are (x,0); on y-axis are (0,y).
- Distance between two points comes from the Pythagoras theorem.
- Midpoint is the section formula with ratio 1:1.
- Three points are collinear if the area of the triangle they form is 0.
- To prove a shape: find side lengths with the distance formula, then compare.
Learn the key ideas Beta
Distance, Quadrants, Reflection, Locus
- Signs of (x, y) give the quadrant: I (+,+), II (−,+), III (−,−), IV (+,−).
- The distance formula comes from Pythagoras: square the x-difference and the y-difference, add, then take the square root.
- For a locus equidistant from points A and B, set PA² = PB². It simplifies to the perpendicular bisector of AB.
Common mistake: Forgetting the square root at the end, or adding coordinates instead of subtracting them inside the brackets.
Section Formula, Midpoint, Centroid
- A point dividing AB internally in ratio m:n is a weighted average of the coordinates of A and B.
- The midpoint is the special case m = n. The centroid is the average of the three vertices.
Common mistake: Multiplying m with A's coordinates. In ratio m:n from A to B, m multiplies B's coordinates.
Area of a Triangle
- Use the vertex formula to find a triangle's area directly from its coordinates.
- Area is always positive, so take the absolute value. Zero area means the three points are collinear.
Common mistake: Forgetting the factor one-half or the absolute value, which gives double the area or a negative area.
Slope and Equations of Lines
- Slope measures steepness. Slope zero gives a horizontal line y = k. A vertical line x = k has undefined slope.
- Parallel lines have equal slopes. For perpendicular lines (neither vertical), the product of the slopes is −1.
- To find intercepts, put y = 0 for the x-intercept and x = 0 for the y-intercept.
Common mistake: Taking slope of ax + by + c = 0 as a/b instead of −a/b; always rewrite as y = mx + c to check.
Triangle Centres and Parallelograms
- The circumcentre is equidistant from all vertices. In a right triangle, it is the midpoint of the hypotenuse.
- The orthocentre is where the altitudes meet. In a right triangle, it is the right-angle vertex.
- A quadrilateral is a parallelogram if its diagonals have the same midpoint, meaning they bisect each other.
Common mistake: Mixing up centroid, circumcentre and orthocentre. They are different points, and coincide only in an equilateral triangle.
Exam tips
- To check whether a point lies on a line, substitute both coordinates and see if the equation holds.
- Draw a quick rough sketch to check quadrants, signs and right angles before calculating.
- For a right triangle, spot the right angle first; the circumcentre and orthocentre follow instantly.
Beta: made with AI and checked by a second AI. A teacher has not reviewed it yet.
Sample questions
What is the distance between the points (3,4) and (0,0)?
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Answer: A. 5
The distance between two points (x1, y1) and (x2, y2) is √((x2-x1)² + (y2-y1)²). Applying to points (3,4) and (0,0), we get √((3-0)² + (4-0)²) = √(9+16) = √25 = 5.
If a line passes through (3,2) with slope 0, what is the equation of the line?
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Answer: A. y = 2
A line with slope 0 is horizontal. It maintains the same y-value throughout, which is 2 at (3,2). Hence, the equation is y = 2.
In which quadrant does the point (-3,-4) lie?
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Answer: C. III
The point (-3,-4) lies in the third quadrant, where both x and y coordinates are negative.
Which of the following points does NOT lie on the line y = 2x + 1?
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Answer: D. (3, 5)
Substitute x values into the line equation y = 2x + 1 and derive y. For (3, 5), y should be 7 to lie on the line, not 5.
Evaluate the equation of a line perpendicular to 2x - 3y = 7, passing through (4, -2).
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Answer: B. 3x + 2y = 10
The perpendicular slope would be reciprocal negative (3/2) of given equation slope (-2/3). Therefore, form y + 2 = 3/2(x - 4) leads to final eq 3x + 2y = 10.
More questions in this quiz
Answers and explanations are in the full quiz.
- What is the midpoint of the line segment joining the points (6,8) and (10,12)?
- Calculate the area of a triangle with vertices at (1,2), (4,6), and (1,6).
- Find the equation of a line passing through the point (1,1) with slope 2.
- Find the coordinates of the centroid of triangle with vertices (0,0), (3,3), and (0,3).
- Find the locus of points equidistant from (5,0) and (9,6).
- The line segment joining (-3, 4) and (1, 2) is divided in the ratio 3:1. Find the coordinates of the point of division.
- What is the slope of the line with equation 4x + 3y = 12?
- Identify the image of the point (4, -3) under reflection in the line y = x.
- Find the equation of the line parallel to y = 3x + 4, passing through (-1, 6).
- Determine the coordinates of the orthocenter of the triangle with vertices (0,0), (2,0), and (0,2).
- Where does the line 5x + 12y = 60 intersect the y-axis?
- Given the vertices of a quadrilateral A(-1, 3), B(2, 1), C(7, 3), D(4, 5), determine if ABCD is a parallelogram.
- Find the circumcenter of the triangle with vertices (0,0), (6,0), and (0,8).
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