Question

Find the distance between the two points rounding to the nearest tenth (if necessary). (8, -4) and (3, 8)

a) 13.4 units
b) 10.4 units
c) 10.2 units
d) 13.0 units

Answer 1

The distance between the points (8, -4) and (3, 8) can be found using the distance formula and is 13.0 units, corresponding to answer choice (d).

Step-by-step explanation:

To calculate the distance between the points (8, -4) and (3, 8), we use the distance formula which is derived from the Pythagorean theorem:

Distance = √[(x2 - x1)² + (y2 - y1)²]

Where (x1, y1) and (x2, y2) are the coordinates of the two points.

1. Subtract the x-coordinates: 3 - 8 = -5
2. Subtract the y-coordinates: 8 - (-4) = 12
3. Square each result: (-5)² = 25 and (12)² = 144
4. Add the squares: 25 + 144 = 169
5. Take the square root of the sum: √169 = 13

So, the distance between the two points is 13.0 units. This matches answer choice (d).