NCERT Class 10 Maths — Chapter 7

Exercise 7.4: Coordinate Geometry Mixed Problems (Optional)

Optional but good practice. Mixed problems combining distance, section, and area formulas.

mixed coordinate geometryapplied problems
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NCERT Questions
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Practice MCQs
2
Key Concepts
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Extra Practice Questions

These questions cover the same concepts as Exercise 7.4. Try solving them to build confidence before or after the textbook exercise.

1

The two opposite vertices of a square are $(-1, 2)$ and $(3, 2)$. Find the other two vertices.

A.$(1, 0)$ and $(1, 4)$
B.$(0, 2)$ and $(2, 2)$
C.$(1, -1)$ and $(1, 5)$
D.$(0, 0)$ and $(2, 4)$
2

The vertices of a triangle are $A(-2, 1)$, $B(5, 4)$, $C(2, -3)$. Find the equation relating coordinates of the centroid.

A.$G = \left(\frac{5}{3}, \frac{2}{3}\right)$
B.$G = (2, 1)$
C.$G = (1, 1)$
D.$G = \left(\frac{7}{3}, \frac{4}{3}\right)$
3

In which quadrant does the point $(-3, 4)$ lie?

A.I
B.II
C.III
D.IV
4

The line joining $(1, -2)$ and $(-3, 4)$ is trisected. Find the coordinates of the two trisection points.

A.$(-\frac{1}{3}, 0)$ and $(-\frac{5}{3}, 2)$
B.$(0, -1)$ and $(-2, 3)$
C.$(-1, 0)$ and $(-2, 2)$
D.$(-\frac{1}{3}, 0)$ and $(-\frac{7}{3}, 2)$
5

A point $P$ divides the line segment joining $A(1, -5)$ and $B(-4, 5)$ externally in ratio $2:3$. Find the coordinates of $P$.

A.$(11, -25)$
B.$(11, 25)$
C.$(-11, 25)$
D.$(-2, -1)$
6

Find the distance between $(a, b)$ and $(-a, -b)$.

A.$2\sqrt{a^2+b^2}$
B.$\sqrt{a^2+b^2}$
C.$2(a+b)$
D.$a+b$
7

Find the distance between $(7, 0)$ and $(-5, 0)$.

A.12
B.2
C.7
D.5
8

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

A.$(4, 6)$
B.$(3, 5)$
C.$(8, 12)$
D.$(2, 2)$
9

Find the point on the x-axis equidistant from $(5, 4)$ and $(-2, 3)$.

A.$(2, 0)$
B.$(3, 0)$
C.$(1, 0)$
D.$(4, 0)$
10

Find the distance between $(\cos\theta, \sin\theta)$ and $(\sin\theta, -\cos\theta)$.

A.$\sqrt{2}$
B.2
C.1
D.$\sqrt{3}$
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Common Mistakes to Avoid

  • ✗Not drawing a rough diagram first
  • ✗Using the wrong formula for the problem type

Other Exercises in Chapter 7

Exercise 7.1
Distance Formula
Exercise 7.2
Section Formula
Exercise 7.3
Area of a Triangle
Exercise 7.4
Coordinate Geometry Mixed Problems (Optional)

Frequently Asked Questions

Is Exercise 7.4 optional?

Yes, it's marked optional in the NCERT textbook.

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