Question

If P=(−2,5) and Q=(1,9), find the distance PQ.
a. 4
b. 5
c. 6
d. 7

Answer 1

Using the distance formula d = √((x2 - x1)^2 + (y2 - y1)^2), the distance between points P=(-2,5) and Q=(1,9) is calculated to be 5 units.Option B is the correct answer.

Step-by-step explanation:

To find the distance between the points P and Q, you can use the distance formula, which is derived from the Pythagorean theorem. The distance formula for two points in a Cartesian coordinate system is d = √((x2 - x1)^2 + (y2 - y1)^2). For points P=(-2,5) and Q=(1,9), you will substitute the x and y coordinates respectively into the formula.

Therefore, the distance PQ is calculated as follows:

1. First, calculate the difference in the x-coordinates: (1 - (-2))^2 = 3^2 = 9.
2. Next, calculate the difference in the y-coordinates: (9 - 5)^2 = 4^2 = 16.
3. Now, add these two results: 9 + 16 = 25.
4. Finally, take the square root of 25 to find the distance: √25 = 5.

So the distance between points P and Q is 5 units, which corresponds to option b.