Question

Practice & Problem Solving O

7. Leveled Practice Use the Pythagorean Theorem
to find the distance between points P and Q.
Label the length, in units, of each leg of the right triangle.
fy
у
c²=
10
8
6
4
2
0
0
P(3, 2)
2
units
4 6
8
Q(9, 10)
10
units
X
C=
2+
2
units.
Scan
Multime
The distance between point P and point Q is

Answer 1

Using the Pythagorean Theorem, the distance between point P (3, 2) and point Q (9, 10) can be found by first finding the length of the legs of the right triangle formed by the horizontal and vertical differences between the two points.

The horizontal difference is (9-3) = 6 units, and the vertical difference is (10-2) = 8 units. Therefore, the length of the legs of the right triangle are 6 units and 8 units.

Using the Pythagorean Theorem (c^2 = a^2 + b^2), where c is the hypotenuse (the distance between P and Q) and a and b are the legs, we can find the distance:

c^2 = 6^2 + 8^2

c^2 = 36 + 64

c^2 = 100

Taking the square root of both sides gives:

c = sqrt(100) = 10

Therefore, the distance between point P and point Q is 10 units.

Explanation: