Question

Find the distance between each pair of points. Round your answer to the nearest tenth, if necessary.

(6,5), (-2,-4)

A) 12
B) 1.7
C) 4.1
D) 3.9

Answer 1

The distance between the points (6,5) and (-2,-4) is calculated using the distance formula, which results in approximately 12.0 units. This is option A).

Step-by-step explanation:

The question involves finding the distance between two points on a Cartesian plane. The two points given are (6,5) and (-2,-4). To calculate the distance, we use the distance formula which is derived from the Pythagorean theorem:

1. Calculate the differences in the x-coordinates and y-coordinates separately:
   Delta x = x2 - x1 = -2 - 6 = -8 and
   Delta y = y2 - y1 = -4 - 5 = -9.
2. Square both differences:
   (Delta x)^2 = (-8)^2 = 64 and
   (Delta y)^2 = (-9)^2 = 81.
3. Add the squares of the differences:
   64 + 81 = 145.
4. Take the square root of the sum to find the distance:
   sqrt(145) = 12.04, which rounds to 12.0 to the nearest tenth.

The distance between the points (6,5) and (-2,-4) is approximately 12.0 units, which corresponds to option A).