Question

• plot the two points

• draw the hypotenuse
• complete the triangle
• use the Pythagorean theorem to find the distance between the
given points
• show all your work
• leave answers in simplest radical form.
1. (3, 4), (-2, 6)
У
61
.
2
10
8 9 10

Answer 1

9514 1404 393

Answer:

√29

Explanation:

We can call the given points A(3, 4) and B(-2, 6).

The right triangle with segment AB as a hypotenuse can best be drawn along grid lines. Then the vertical leg is the difference of y-coordinates: 6-4 = 2, and the horizontal leg is the difference of x-coordinates: 3 -(-2) = 5.

The Pythagorean theorem tells you the square of the hypotenuse is the sum of the squares of the legs.

AB² = 2² + 5²

AB² = 4 + 25 = 29

Taking the square root, we find the length of the line segment between the points to be ...

AB = √29