Question

Determine the length of the line segment shown.

graph of line segment from negative 3 comma negative 2 to 0 comma 2

4 units
5 units
10 units
25 units

Answer 1

I think the answer is 5

Explanation:

Answer 2

(b) 5 units

Explanation:

You want to know the length of the segment from (-3, -2) to (0, 2).

Distance

The formula for the distance between two points is based on the Pythagorean theorem. The distance is the root of the sum of the squares of the horizontal distance and the vertical distance.

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Application

For the given points, the distance is computed to be ...

`d=√((0-(-3))^2+(2-(-2))^2)=√(3^2+4^2)=√(9+16)=√(25)\\\\d=5`

The line segment is 5 units long.

__

Additional comment

The numbers (3, 4, 5) comprise a "Pythagorean triple", a set of three integers that satisfy the Pythagorean relation. You will see the 3-4-5 right triangle a lot in algebra and geometry problems, along with its multiples, such as 6-8-10.

You don't have to go to the trouble of using the formula. You can count grid squares on the graph to see the triangle is a 3-4-5 triangle.