In the distance formula, the two legs of the right triangle formed by points $P_1$ and $P_2$ represent which quantities?

The horizontal and vertical changes between the two points

The sum and difference of the coordinates

The slopes and intercepts of the line

The midpoints of each coordinate axis

Using the Pythagorean Theorem Practice — Grade 7 math

Section 7.5: Using the Pythagorean Theorem — Practice Questions

1. Using the distance formula, what is the distance between the points $(1, 2)$ and $(7, 10)$?
- A. $10$
- B. $\sqrt{28}$
- C. $\sqrt{100}$
- D. $14$
2. The distance between the points $(-3, 4)$ and $(5, -2)$ is $\_\_\_$.
3. Which expression correctly represents the distance between $(-4, -1)$ and $(2, 7)$?
- A. $\sqrt{36 + 64}$
- B. $\sqrt{4 + 16}$
- C. $\sqrt{36 + 16}$
- D. $\sqrt{64 + 4}$
4. Two points $(-6, 3)$ and $(-6, -9)$ lie on a vertical line. The distance between them is $\_\_\_$.
5. In the distance formula, the two legs of the right triangle formed by points $P_1$ and $P_2$ represent which quantities?
- A. The horizontal and vertical changes between the two points
- B. The sum and difference of the coordinates
- C. The slopes and intercepts of the line
- D. The midpoints of each coordinate axis
6. Find the perimeter of the triangle with vertices $A(-1, 2)$, $B(5, 4)$, and $C(1, -4)$.
- A. $4\sqrt{10} + 4\sqrt{5}$
- B. $2\sqrt{10} + 2\sqrt{5}$
- C. $8\sqrt{10}$
- D. $4\sqrt{10} + 2\sqrt{5}$
7. Calculate the distance between the points $(1, 2)$ and $(9, 17)$. The distance is ___.
8. What is the distance between the points $(-3, 5)$ and $(4, -19)$? The distance is ___.
9. Which expression correctly represents the distance between points $(-2, 5)$ and $(3, -7)$?
- A. $d = \sqrt{(3 - (-2))^2 + (-7 - 5)^2}$
- B. $d = \sqrt{(3 + (-2))^2 + (-7 + 5)^2}$
- C. $d = \sqrt{(-2 - 5)^2 + (3 - (-7))^2}$
- D. $d = \sqrt{(3 - 5)^2 + (-7 - (-2))^2}$
10. Find the distance from the origin, $(0, 0)$, to the point $(9, -12)$. The distance is ___.