Question

1.) Find the DISTANCE between point (12, -1) and point (10,10).

2.) Find the MIDPOINT between point (-5,11) and point (-9,-6).
a) 11.4, (-7, 2.5)
b) 11.7, (-7, 2.5)
c) 13, (-7, 2.5)
d) 13.5, (-7, 2.5)

Answer 1

The distance between the two points (12, -1) and (10, 10) is approximately 11.180 units. The distance between the two points (-5, 11) and (-9, -6) is approximately 17.464 units.

Step-by-step explanation:

To find the distance between two points, you can use the distance formula, which is derived from the Pythagorean theorem. The formula is: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)

For the first question, the points are (12, -1) and (10, 10). Plugging these values into the formula gives: d = sqrt((10 - 12)^2 + (10 - (-1))^2) = sqrt((-2)^2 + (11)^2) = sqrt(4 + 121) = sqrt(125) = 11.180

Therefore, the distance between the two points is approximately 11.180 units.

For the second question, the points are (-5, 11) and (-9, -6). Plugging these values into the formula gives: d = sqrt((-9 - (-5))^2 + (-6 - 11)^2) = sqrt((-4)^2 + (-17)^2) = sqrt(16 + 289) = sqrt(305) = 17.464

Therefore, the distance between the two points is approximately 17.464 units.