Find the distance between (4, -2) and (-2, 3) to the nearest tenth. Group of answer choices0.0 units-1.0 units3.4 units7.8 units
Question
Find the distance between (4, -2) and (-2, 3) to the nearest tenth.
Group of answer choices:
- 0.0 units
- -1.0 units
- 3.4 units
- 7.8 units
Solution
To find the distance between two points in a plane, we can use the distance formula which is derived from the Pythagorean theorem. The distance d between two points (x1, y1) and (x2, y2) is given by:
d = sqrt[(x2-x1)² + (y2-y1)²]
Here, our points are (4, -2) and (-2, 3). So, x1 = 4, y1 = -2, x2 = -2, and y2 = 3.
Substituting these values into the formula, we get:
d = sqrt[(-2-4)² + (3-(-2))²] d = sqrt[(-6)² + (5)²] d = sqrt[36 + 25] d = sqrt[61]
The square root of 61 is approximately 7.8. So, the distance between the points (4, -2) and (-2, 3) is approximately 7.8 units. Therefore, the correct answer is 7.8 units.
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