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

Answer:

$\sqrt{85}$.

Step-by-step 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.)

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