Question

Find the distance between each pair of points (-4,6) and (3,-7)

Answer 1

Here is your answer . Hope this helps you.

Answer 2

`\boxed {\boxed {\sf √(218) \ or \ 14.76}}`

Explanation:

The formula for calculating the distance between 2 points is:

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

In this formula, (x₁, y₁) and (x₂, y₂) are the 2 points. The 2 points we are given are (-4, 6) and (3, -7). If we match the value with the corresponding variable we see that:

• x₁ = -4
• y₁ = 6
• x₂ = 3
• y₂ = -7

Substitute the values into the formula.

`d= \sqrt{(3 - -4)^2 + (-7-6)^2`

Solve inside the parentheses.

• (3--4) = (3+4) = 7
• (-7-6) = -13

`d=\sqrt {(7)^2 + (-13)^2`

Solve the exponents.

• (7)²= 7*7 = 49
• (-13)² = -13 * -13 = 169

`d= \sqrt{ (49)+(169)`

Add.

`d= √(218)`

`d=14.76482306`

If we round to the nearest hundredth place, the 4 in the thousandth place tells us to leave the 6.

`d \approx 14.76`

The distance between the points (-4, 6) and (3, -7) is √218 or approximately 14.76.