Question

Find x so that the distance between the points (-2, -3) and (-3, x) is equal to 5.

Answer 1

Step-by-step explanation:

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Answer 2

The value of x is 2√6 - 3.

Given:

P1 (-2, -3)

P2 (-3, x)

Distance = 5 units

To find: x

Solution:

We are given P1 (-2, -3) and P2 (-3, x)

x₁ = -2

x₂ = -3

y₁ = -3

y₂ = x

According to the distance formula,

Distance = $\sqrt{(x_{2}-x_{1} )^2 + (y_{2} -y_{1} )^2}$

Putting the values of the variables,

Distance = $\sqrt{(-2-(-3) )^2 + (x -(-3))^2}$

⇒ Distance = $\sqrt{(1 )^2 + (x +3)^2}$

⇒ $\sqrt{(1 )^2 + (x +3)^2}$ = 5 (given that distance = 5 units)

Squaring both sides, we get

1 + (x + 3)² = 25

⇒ (x + 3)² = 24

⇒ x + 3 = 2√6

⇒ x = 2√6 - 3

∴ The value of x is 2√6 - 3.

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