Question

Find the length of the segment that joins the points (-5, 4) and (6,-3).

Answer 1

`\boxed {\boxed {\sf d=√(170) \ or \ d\approx 13.04}}}`

Explanation:

We are asked to find the length of a segment or the distance between the 2 points. The formula for distance is:

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

where (x₁ y₁) and (x₂, y₂) are the points. We are given the points ( -5, 4) and (6, -3). If we match the number and the corresponding variable, it is:

• x₁= -5
• y₁= 4
• x₂= 6
• y₂ = -3

Substitute the values into the formula.

`d= \sqrt{(6--5)^2+(-3-4)^2`

Solve inside the parentheses.

• 6--5 (Back to back negative signs become a positive)= 6+5 =11
• -3-4= -7

`d= \sqrt{(11)^2+(-7)^2`

Solve the exponents.

• (11)²= 11*11= 121
• (-7)²= -7*-7= 49

`d= \sqrt {(121)+(49)`

Add.

`d= \sqrt {170}`

`d=13.0384048104`

Even though it's not specified, we could round to the nearest hundredth to make the answer more concise. The 8 in the thousandth place tells us to round the 3 to a 4 in the hundredth place.

• 13.0384048104

`d\approx 13.04`

The length of the segment is √170 or approximately 13.04.