NCERT Class 10 Maths — Chapter 7

Exercise 7.3: Area of a Triangle

Calculate the area of a triangle given three vertices using the coordinate formula. Also check if three points are collinear (area = 0).

area using coordinatescollinearityarea formula
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Extra Practice Questions

These questions cover the same concepts as Exercise 7.3. Try solving them to build confidence before or after the textbook exercise.

1

The coordinates of the point which divides the line segment joining $(1, 3)$ and $(5, 7)$ in the ratio $1:1$ are:

A.$(3, 5)$
B.$(2, 4)$
C.$(4, 6)$
D.$(6, 10)$
2

The vertices of a triangle are $A(2, 3)$, $B(4, -1)$, $C(1, 2)$. Find the length of the median from $A$.

A.$\frac{\sqrt{26}}{2}$
B.$\sqrt{10}$
C.$\frac{\sqrt{5}}{2}$
D.$\sqrt{5}$
3

Find the area of the quadrilateral with vertices $(1, 1)$, $(7, -3)$, $(12, 2)$, and $(7, 21)$ by dividing into two triangles.

A.132 sq. units
B.66 sq. units
C.99 sq. units
D.264 sq. units
4

Find the centroid of a triangle with vertices $(0, 0)$, $(6, 0)$, and $(0, 9)$.

A.$(2, 3)$
B.$(3, 3)$
C.$(3, 4.5)$
D.$(6, 9)$
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 area of the triangle with vertices $(1, 2)$, $(4, 6)$, and $(5, 2)$.

A.8 sq. units
B.6 sq. units
C.10 sq. units
D.12 sq. units
7

Find the distance between $(1, 1)$ and $(4, 5)$.

A.5
B.3
C.4
D.7
8

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

A.$(2, 0)$
B.$(3, 0)$
C.$(1, 0)$
D.$(4, 0)$
9

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

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

Determine if the points $A(1, 2)$, $B(5, 4)$, $C(3, 8)$, and $D(-1, 6)$ form a square.

A.Yes, all sides = $\sqrt{20}$ and diagonals = $\sqrt{40}$
B.No, sides are unequal
C.It's a rectangle but not a square
D.It's a rhombus but not a square

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Common Mistakes to Avoid

  • Errors in the determinant-style formula expansion
  • Forgetting the ½ multiplier
  • Getting a negative area (take absolute value)

Other Exercises in Chapter 7

Frequently Asked Questions

How do you find area of a triangle using coordinates?

Area = ½|x₁(y₂-y₃) + x₂(y₃-y₁) + x₃(y₁-y₂)|. If this equals 0, the points are collinear.

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