Question

What is the exact distance from (−1, 4) to (6, −2)? square root of 80. units square root of 82. units square root of 85. units square root of 89. units

Answer 1

C

Explanation:

Answer 2

`√(85)`.

Explanation:

`x`-coordinates:

• First point:
  `-1`.
• Second point:
  `6`.
• Difference:
  `|-1 - 6| = |-7| = 7`.

`y`-coordinates:

• First point:
  `4`.
• Second point:
  `-2`.
• Difference:
  `|4 - (-2)| = |6| = 6`.

Refer to the diagram attached. Consider these two points as the two end points of the hypotenuse of a right triangle. The lengths of the two legs are equal to:

• the difference between the two
  `x`-coordinates,
  `7`, and
• the difference between the two
  `y`-coordinates,
  `6`.

Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)

`\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= √(7^2 + 6^2) \\ &= √(85)\end{aligned}`.