Question

The distance between the points (–2, 5) and (5, –2) is ______.

विकल्प

• `7sqrt(2)`

• 14

• `2sqrt(7)`

• 7

Answer 1

The distance between the points (–2, 5) and (5, –2) is `underlinebb(7sqrt(2))`.

Explanation:

1. Identify the coordinates

Let the two points be:

P₁(x₁, y₁) = (–2, 5)

P₂(x₂, y₂) = (5, –2)

2. Apply the distance formula

The distance d between two points is given by:

`d = sqrt((x_2 - x_1)^2 + (y_2 - y_1)^2`

3. Substitute and calculate

Substitute the coordinates into the formula:

`d = sqrt((5 - (-2))^2 + (-2 - 5)^2`

`d = sqrt((5 + 2)^2 + (-7)^2`

`d = sqrt(7^2 + (-7)^2`

`d = sqrt(49 + 49)`

`d = sqrt(98)`

4. Simplify the radical

Simplify `sqrt(98)` by factoring out the largest perfect square:

`d = sqrt(49 xx 2)`

`d = 7sqrt(2)`