Class 10 • Maths • Chapter 7
Coordinate Geometry
True & False Quiz
Distance. Section. Area.
✓True
✗False
25
Questions
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Ch.7
Chapter
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X
Class
Why True & False for Coordinate Geometry?
How this format sharpens your conceptual clarity
🔵 Coordinate Geometry bridges algebra and geometry — every shape, distance, and division can be computed using just coordinates.
✅ T/F tests the distance formula, section formula, and area of triangle — three formulas with subtle sign and order traps.
🎯 The midpoint formula is the section formula with m:n = 1:1 — always cross-check using this relationship.
📋
Read each statement carefully. Click True or False — instant feedback with explanation appears. Submit anytime; unattempted questions are marked Skipped.
Q 1
The distance between two points on the x-axis is the difference of their x-coordinates.
Q 2
The distance between \((x_1,y_1)\) and \((x_2,y_2)\) in the plane is given by \((x_2-x_1)^2+(y_2-y_1)^2\).
Q 3
If the distance between two distinct points in a plane is zero, then they are collinear.
Q 4
The midpoint of the line segment joining \((x_1,y_1)\) and \((x_2,y_2)\) is \(\left(\frac{x_1+x_2}{2},\ \frac{y_1+y_2}{2}\right)\).
Q 5
Any point on the y-axis has coordinates of the form (x,0)(x,0).
Q 6
A point in the second quadrant has positive x-coordinate and negative y-coordinate.
Q 7
If a point divides a line segment internally in the ratio\( m_1:m_2\), the x-coordinate is \(\frac{m_1x_2+m_2x_1}{m_1+m_2}\).
Q 8
The section formula can only be used for internal division of a line segment.
Q 9
If the coordinates of the endpoints of a segment are known, its midpoint always lies between them on the same line.
Q 10
Three points form a triangle of non-zero area if and only if they are collinear.
Q 11
If the area of a triangle with vertices \((x_1,y_1),(x_2,y_2),(x_3,y_3)\) is zero, then the three points are collinear.
Q 12
The formula for the area of a triangle with vertices \((x_1,y_1),(x_2,y_2),(x_3,y_3)\) involves only the x-coordinates of the vertices.
Q 13
If two vertices of a triangle are fixed and the third vertex moves along a line parallel to the segment joining the fixed vertices, the area of the triangle remains constant.
Q 14
For a line segment, if a point divides it in the ratio 1:1, the point is the midpoint of the segment.
Q 15
If \((x_1,y_1)\) and \((x_2,y_2)\) are symmetric about the y-axis, then \(x_2=-x1\) and \(y_2=y_1\).
Q 16
A point in the first quadrant always has a negative y-coordinate.
Q 17
If a point lies on the x-axis, its ordinate is zero.
Q 18
The distance formula in coordinate geometry is derived from the Pythagoras theorem.
Q 19
If two points have the same x-coordinate, the line joining them is parallel to the x-axis.
Q 20
The coordinates of any point on the line segment joining \((x_1,y_1\) and \((x_2,y_2)\) can be expressed using the section formula for some positive ratio.
Q 21
In the coordinate plane, the origin is the point where the graph of every line passes.
Q 22
If the area of a triangle formed by three points is zero, at least two points must coincide.
Q 23
The coordinates of the centroid of a triangle with vertices \((x_1,y_1),(x_2,y_2),(x_3,y_3)\) is \(\left(\frac{(x_1+x_2+x_3}{3},\frac{y_1+y_2+y_3}{3}\right)\).
Q 24
In coordinate geometry, the abscissa of a point is its y-coordinate.
Q 25
If a point lies in the third quadrant, both its coordinates are negative.
Key Takeaways — Coordinate Geometry
Core facts for CBSE Boards & exams
1
Distance = √[(x₂−x₁)² + (y₂−y₁)²].
2
Section formula (internal): x = (mx₂+nx₁)/(m+n), y = (my₂+ny₁)/(m+n).
3
Midpoint = ((x₁+x₂)/2, (y₁+y₂)/2) — special case of section formula.
4
Area of triangle = ½|x₁(y₂−y₃) + x₂(y₃−y₁) + x₃(y₁−y₂)|.
5
Three points are collinear iff the area of the triangle they form is ZERO.
6
Distance from origin to (a,b) = √(a²+b²).