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Chapter 7: Coordinate Geometry

    Introduction

    Distance Between Two Points

    Distance Between Two Points on a Line Parallel To The Coordinate Axis

    Distance Between Any Two Points In the X-Y Plane

    Section Formula

    TriSectional Points of a Line

    Centroid Triangle

    Area of the Triangle

    Straight Lines

    Summary

    Enhanced Curriculum Support

    Easy Level Worksheet

    Moderate Level Worksheet

    Hard Level Worksheet

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Chapter 7: Coordinate Geometry > Easy Level Worksheet

Easy Level Worksheet

Very Short Answer Questions (1 Mark Each)

(1) Write the coordinates of the origin.

(2) What is the distance between the points A(3, 4) and B(3, -4)?

Correct! Since both points have the same x-coordinate, distance = |4 - (-4)| = 8 units.

(3) What is the formula for finding the distance between two points x1,y1 and x2,y2?

Perfect! This is the distance formula derived from the Pythagorean theorem.

(4) Find the distance of the point (0, 5) from the origin.

Excellent! Distance = 0−02+5−02 = 25 = 5 units.

Short Answer Questions (2 Marks Each)

Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.

(1) Find the distance between the points A(1, 2) and B(4, 6). Distance =

Perfect! Distance = 4−12+6−22 = 9+16 = 25 = 5 units.

(2) If the point A(2, y) lies on the y-axis, find the value of y. This is

Correct! A point on the y-axis must have x-coordinate = 0, but A has x = 2, so it cannot lie on the y-axis.

(3) Find the coordinates of the point which lies on the x-axis at a distance of 5 units from the origin. Points are and

Excellent! Points on x-axis have y = 0, and distance 5 from origin gives us (±5, 0).

(4) Find the length of the line segment joining the points (-2, 1) and (3, 5). Length =

Perfect! Distance = 3−−22+5−12 = 25+16 = 41 units.

Long Answer Questions (4 Marks Each)

Note: Answer each question with steps and explanation. Write down the answers on sheet and submit to the school subject teacher.

(1) Show that the points A(1, 2), B(4, 6), C(7, 10) lie on the same line.

(2) Find the coordinates of a point that divides the line joining (2, 3) and (6, 7) in the ratio 1:1. Coordinates =

Perfect! For ratio 1:1, we find the midpoint: (2+62, 3+72) = (4, 5).

(3) Find the distance between the points (-3, -4) and (4, 2). Also, find the midpoint of the line segment joining them. Distance = and Midpoint = (In case of fractional coordinates, enter decimal forms)

Excellent! Distance = 4−−32+2−−42 = 49+36 = 85, and midpoint = (−3+42, −4+22) = (0.5, -1).

Part B: Objective Questions (1 Mark Each)

Choose the correct answer and write the option (a/b/c/d)

(1) The coordinates of the origin are

(a) (1, 1) (b) (0, 1) (c) (0, 0) (d) (1, 0)

(1, 1)
(0, 1)
(0, 0)
(1, 0)

Correct! The origin is the intersection of x-axis and y-axis at (0, 0).

(2) The distance between the points (1, 1) and (4, 5) is

(a) 5 (b) 4 (c) 3 (d) 6

5
4
3
6

Correct! Distance = 4−12+5−12 = 9+16 = 25 = 5.

(3) The x-coordinate of any point on the y-axis is

(a) 1 (b) 0 (c) y (d) Cannot say

1
0
y
Cannot say

Correct! All points on the y-axis have x-coordinate = 0.

(4) The midpoint of the line joining (2, 4) and (6, 8) is

(a) (4, 6) (b) (5, 7) (c) (3, 6) (d) (2, 8)

(4, 6)
(5, 7)
(3, 6)
(2, 8)

Correct! Midpoint = (2+62, 4+82) = (4, 6).

(5) The formula for the midpoint of a line joining (x_1, y_1) and (x_2, y_2) is

(a) (x1x22, y1y22) (b) (x1+x22, y1+y22) (c) (x1+x2, y1+y2) (d) (x2−x12, y2−y12)

((x_1x_2)/2, (y_1y_2)/2)
((x_1+x_2)/2, (y_1+y_2)/2)
(x_1 + x_2, y_1 + y_2)
((x_2-x_1)/2, (y_2-y_1)/2)

Correct! The midpoint formula averages the x and y coordinates.

(6) If a point lies in the 3rd quadrant, its coordinates are

(a) (+, +) (b) (+, –) (c) (–, +) (d) (–, –)

(+, +)
(+, –)
(–, +)
(–, –)

Correct! In the 3rd quadrant, both x and y coordinates are negative.

(7) Which of these points lies on the x-axis?

(a) (0, 5) (b) (5, 0) (c) (3, 4) (d) (0, 0)

(0, 5)
(5, 0)
(3, 4)
(0, 0)

Correct! Points on the x-axis have y-coordinate = 0, so (5, 0) lies on the x-axis.

(8) The distance between (0, 0) and (6, 8) is

(a) 8 (b) 10 (c) 14 (d) 12

8
10
14
12

Correct! Distance = 62+82 = 36+64 = 100 = 10 units.

(9) In which quadrant does the point (-3, -2) lie?

(a) I (b) II (c) III (d) IV

I
II
III
IV

Correct! Since both coordinates are negative, the point lies in the 3rd quadrant.

(10) The point which lies at equal distance from the x-axis and y-axis is

(a) (1, –1) (b) (3, 3) (c) (–2, –2) (d) All of these

(1, –1)
(3, 3)
(–2, –2)
All of these

Correct! Points equidistant from both axes have |x| = |y|, so all given points satisfy this condition.
Distance formula
(0, 0)
Midpoint formula
x-axis
Quadrant I
y-axis
Quadrant III
√[(x_2-x_1)² + (y_2-y_1)²]
Formulas and Calculations
Axes and Origin
Quadrants and Regions

Coordinate Geometry Challenge

Determine whether these statements about coordinate geometry are True or False:

The distance formula is √[(x_1+x_2)² + (y_1+y_2)²]
Points on the y-axis have y-coordinate = 0
The origin has coordinates (0, 0)
In quadrant III, both coordinates are negative
The midpoint of (2, 4) and (6, 8) is (4, 6)
All points with equal x and y coordinates lie on the x-axis

Coordinate Geometry Quiz