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Lesson 7-5: Distance on the Coordinate Plane — Practice Questions

  1. 1. The horizontal distance between two points is 8 units and the vertical distance is 15 units. The straight-line distance between the points is ___ units.

  2. 2. To find the distance $c$ between two points with horizontal distance $a$ and vertical distance $b$, which formula correctly applies the Pythagorean Theorem?

    • A. $c = a + b$
    • B. $c = a^2 + b^2$
    • C. $c = \sqrt{a^2 + b^2}$
    • D. $c = \sqrt{a+b}$
  3. 3. A right triangle is formed between two points on a coordinate plane. If the horizontal leg is 3 units and the vertical leg is 5 units, the exact straight-line distance is ___ units.

  4. 4. Two points have a vertical distance of 7 units and a horizontal distance of 24 units. What is the straight-line distance between them? ___ units.

  5. 5. The horizontal distance between two points is 6 units and the vertical distance is 3 units. What is the exact distance between the points?

    • A. 9
    • B. 45
    • C. $\sqrt{45}$
    • D. $\sqrt{9}$
  6. 6. What is the distance between point $A(1, 2)$ and point $B(10, 14)$ on the coordinate plane? The distance is ___ units.

  7. 7. Find the distance between points $M(2, -4)$ and $N(9, 1)$. Express your answer as a radical.

  8. 8. What is the exact distance between the origin, point $O(0, 0)$, and point $P(8, -15)$? The distance is ___ . (a number)

  9. 9. A drone flies in a straight line from a starting point at $(1, 1)$ to a delivery location at $(7, 9)$. What is the total distance the drone traveled?

    • A. 8 units
    • B. 10 units
    • C. 14 units
    • D. 100 units
  10. 10. On a treasure map, the starting point is at $(-6, -2)$ and the treasure is at $(6, 3)$. What is the straight-line distance to the treasure? The distance is ___ units.