NCERT Class 10 Maths — Chapter 7

Exercise 7.1: Distance Formula

Find distances between points on the coordinate plane. Check if three points form a triangle, a line, or specific shapes.

distance formuladistance between two pointscollinear points
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Extra Practice Questions

These questions cover the same concepts as Exercise 7.1. Try solving them to build confidence before or after the textbook exercise.

1

The origin has coordinates:

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

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.$(6, 10)$
3

The vertices of a triangle are $(2, 1)$, $(5, 2)$, and $(3, 4)$. Find its centroid.

A.$\left(\frac{10}{3}, \frac{7}{3}\right)$
B.$(3, 2)$
C.$(4, 3)$
D.$\left(\frac{7}{3}, \frac{10}{3}\right)$
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

The distance of the point $(5, 12)$ from the origin is:

A.13
B.17
C.7
D.15
6

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.$\sqrt{5}$
7

If $A(4, -8)$, $B(3, 6)$, and $C(5, -4)$ are the vertices of a triangle, find the length of the median from $B$.

A.$\frac{3\sqrt{65}}{2}$
B.$\sqrt{85}$
C.$\sqrt{73}$
D.$\sqrt{61}$
8

The section formula gives the coordinates of a point dividing a line segment in ratio $m:n$ as:

A.$\left(\frac{mx_2+nx_1}{m+n}, \frac{my_2+ny_1}{m+n}\right)$
B.$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$
C.$\left(\frac{mx_1+nx_2}{m+n}, \frac{my_1+ny_2}{m+n}\right)$
D.$\left(\frac{mx_2-nx_1}{m-n}, \frac{my_2-ny_1}{m-n}\right)$
9

The centroid of a triangle with vertices $(x_1, y_1)$, $(x_2, y_2)$, $(x_3, y_3)$ is:

A.$\left(\frac{x_1+x_2+x_3}{3}, \frac{y_1+y_2+y_3}{3}\right)$
B.$\left(\frac{x_1+x_2}{2}, \frac{y_1+y_2}{2}\right)$
C.$(x_1+x_2+x_3, y_1+y_2+y_3)$
D.$\left(\frac{x_1 \cdot x_2 \cdot x_3}{3}, \frac{y_1 \cdot y_2 \cdot y_3}{3}\right)$
10

If the point $P(x, y)$ is equidistant from $A(7, 1)$ and $B(3, 5)$, find the relation between $x$ and $y$.

A.$x - y = 2$
B.$x + y = 2$
C.$x - y = -2$
D.$x + y = 6$

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Common Mistakes to Avoid

  • Sign errors when subtracting coordinates
  • Forgetting to take the square root at the end
  • Not squaring negative differences correctly

Other Exercises in Chapter 7

Frequently Asked Questions

What is the distance formula?

The distance between points (x₁, y₁) and (x₂, y₂) is √[(x₂-x₁)² + (y₂-y₁)²].

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