Answer:
[tex]\sqrt{85}[/tex].
Step-by-step explanation:
[tex]x[/tex]-coordinates:
- First point: [tex]-1[/tex].
- Second point: [tex]6[/tex].
- Difference: [tex]|-1 - 6| = |-7| = 7[/tex].
[tex]y[/tex]-coordinates:
- First point: [tex]4[/tex].
- Second point: [tex]-2[/tex].
- Difference: [tex]|4 - (-2)| = |6| = 6[/tex].
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 [tex]x[/tex]-coordinates, [tex]7[/tex], and
- the difference between the two [tex]y[/tex]-coordinates, [tex]6[/tex].
Apply Pythagorean Theorem to find the length of the hypotenuse (which is equal to the distance between the two points in question.)
[tex]\begin{aligned}\text{Hypotenuse} &= \sqrt{(\text{First Leg})^2 + (\text{Second Leg})^2} \\ &= \sqrt{7^2 + 6^2} \\ &= \sqrt{85}\end{aligned}[/tex].
