Sample Problems on Distance Between Two Points

Problem 1: Find the distance between points A (4, 6) and B(1, 0).

Solution:

Given: A(4, 6) and B(1, 0).

Now we find the distance between the given points that is A and B

So we use the formula

D = [Tex]\sqrt{{(a-p)}^2+{(b-q)}^2}  [/Tex]

Now put the value in the formula

⇒ AB = [Tex]\sqrt{{(4-1)}^2+{(6-0)}^2} [/Tex]

= [Tex]\sqrt{3^2 + 6^2} [/Tex]

= [Tex]\sqrt{45}[/Tex] units

= 3√5 units

Problem 2: Find the distance between points P(4, 0) and Q(1, 0).

Solution:

Given: P(4, 0) and Q(1, 0).

Now we find the distance between the given points that is P and Q

So we use the formula

D = [Tex]\sqrt{{(a-p)}^2+{(b-q)}^2}  [/Tex]

Now put the value in the formula

⇒ PQ = [Tex]\sqrt{{(4-1)}^2+{(0-0)}^2} [/Tex]

= [Tex]\sqrt{3^2 + 0^2} [/Tex]

= [Tex]\sqrt{9}              [/Tex] units

= 3 units

Problem 3: Given points A(3, 0, 4) and B(1, 0, 3). Find the distance between them.

Solution:

Given: A(3, 0, 4) and B(1, 0, 3).

Now we find the distance between the given points that is A and B

Using formula [Tex]\bold{Distance = \sqrt{(x_2 – x_1)^2 + (y_2 – y_1)^2 + (z_2 – z_1)^2}} [/Tex]

⇒ AB = [Tex]\sqrt{{(3-1)}^2+{(0-0)}^2+{(4-3)}^2} [/Tex]

⇒ AB= [Tex]\sqrt{2^2 + 0^2 + 1^2} [/Tex]

⇒ AB= [Tex]\sqrt{5}      [/Tex] units

Thus, distance between A and B is √5 units.

Problem 4: Given points P(6, 0) and R(4, 0). Find the distance between them.

Solution:

Given: P(6, 0) and R(4, 0).

Now we find the distance between the given points that is P and R

So we use the formula

D = [Tex]\sqrt{{(a-p)}^2+{(b-q)}^2}  [/Tex]

Now put the value in the formula

⇒ PR = [Tex]\sqrt{{(6-4)}^2+{(0-0)}^2} [/Tex]

= [Tex]\sqrt{2^2 + 0^2} [/Tex]

= 2 units

Problem 5: Find the distance between the points (12, 0) and (4, 0).

Solution:

Given: P(12, 0) and R(4, 0).

Now we find the distance between the given points that is P and R

So we use the formula

D = [Tex]\sqrt{{(a-p)}^2+{(b-q)}^2}  [/Tex]

Now put the value in the formula

⇒ PR = [Tex]\sqrt{{(12-4)}^2+{(0-0)}^2} [/Tex]

= [Tex]\sqrt{8^2 + 0^2} [/Tex]

= 8 units

Problem 6: Find the distance between the points (12, 0) and (10, 0).

Solution:

Given: A(12, 0) and B(10, 0).

Now we find the distance between the given points that is A and B

So we use the formula

D = [Tex]\sqrt{{(a-p)}^2+{(b-q)}^2}  [/Tex]

Now put the value in the formula

⇒ AB = [Tex]\sqrt{{(12-10)}^2+{(0-0)}^2} [/Tex]

= [Tex]\sqrt{2^2 + 0^2} [/Tex]

= 2 units

Distance Between Two Points is the length of line segment that connect any two points in coordinate plane in coordinate geometry. It can be calculated using distance formula for 2D or 3D. It represents the shortest path between two locations in a given space.

In this article, we will learn how to find the distance between two points. Let’s first understand what are point before learning the methods and formula to find the distance between them.