9514 1404 393
Answer:
- distance between points: √85
- leg 1 (AC) = 7 units
- leg 2 (BC) = 6 units
- hypotenuse (AB) = √85 units
Step-by-step explanation:
When the points are not on the same horizontal or vertical line, a right triangle can be formed by a horizontal line through one point and a vertical line through the other point. Here, we have labeled the given points A and B, and identified the intersection of those horizontal and vertical lines as point C.
__
Leg 1 will be AC. Its length is the difference of the x-coordinates of A and C (or A and B, if you like): 6 -(-1) = 7.
Leg 2 will be BC. Its length is the difference of the y-coordinates of the points: (4 -(-2)) = 6.
The hypotenuse is AB. Its length is given by the Pythagorean theorem as ...
AB² = AC² +BC²
AB² = 7² +6² = 49 +36 = 85 . . . . . fill in the numbers
AB = √85 . . . . . . . . . . . . . . . . . . take the square root
The length of the hypotenuse AB is √85.
