Coordinate Geometry (Case Study) (10 Mathematics)

Real-world coordinate geometry problems involving distances, areas, and straight lines. Applications include map navigation, construction, and architecture

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TL;DR: Real-world coordinate geometry problems involving distances, areas, and straight lines. Applications include map navigation, construction, and archite…

Written & reviewed by the Syllab.in Academic Team (CBSE/NCERT subject experts) · Updated Jul 23, 2026

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Real-world coordinate geometry problems involving distances, areas, and straight lines. Applications include map navigation, construction, and architecture

Coordinate Geometry (Case Study) MCQs with Answers & Explanations

Q1. A surveyor maps a triangular plot with vertices at A(0,0), B(6,0), and C(3,4). What is the area of this plot?

6 sq units
12 sq units ✓ (correct)
18 sq units
24 sq units

Q2. Two towns are located at coordinates (0,0) and (8,6) on a map. What is the straight-line distance between them in units?

10 units ✓ (correct)
12 units
14 units
15 units

Q3. A line passes through points (1,2) and (5,10). What is the slope of this line?

1
2 ✓ (correct)
3
4

Q4. If a line has slope 2 and passes through the point (3,7), what is the equation of the line in the form y = mx + c?

y = 2x + 1 ✓ (correct)
y = 2x + 3
y = 2x + 7
y = 3x + 1

Q5. Points P(1,1), Q(4,4), and R(7,7) are collinear. This means what?

They form a right angle
They lie on the same straight line ✓ (correct)
They form an equilateral triangle
They are at equal distances from origin

Q6. A rectangle has vertices at (0,0), (5,0), (5,3), and (0,3). What is its perimeter?

8 units
15 units
16 units ✓ (correct)
20 units

Q7. The midpoint of a line segment joining (2,4) and (6,8) is?

(3,5)
(4,6) ✓ (correct)
(5,7)
(4,5)

Q8. Which of the following lines is parallel to y = 3x + 2?

y = 3x - 5 ✓ (correct)
y = 2x + 3
y = -3x + 2
y = (1/3)x + 2

Frequently Asked Questions

How do we find the equation of a line given two points?

First, calculate the slope m = (y2-y1)/(x2-x1). Then use the point-slope form y - y1 = m(x - x1) with either point, or solve for the y-intercept c using y = mx + c. Alternatively, use the two-point form: (y - y1)/(y2 - y1) = (x - x1)/(x2 - x1), which directly gives the line equation.

What is the significance of the y-intercept in the equation y = mx + c?

The y-intercept (value c) represents the point where the line crosses the y-axis, at coordinates (0, c). It shows the value of y when x = 0. The slope m tells us how steeply the line rises or falls, and the y-intercept gives us a reference point to graph the line.

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