Question

What is the exact distance between the points (4,-2) and (-6,4)?

Select the correct answer.
O 4√10
O2√34
O2√26
O 10√6

Answer 1

To calculate the distance between points (4,-2) and (-6,4), apply the distance formula to yield an exact distance of 2∙√34 units.

Step-by-step explanation:

The exact distance between the points (4,-2) and (-6,4) can be determined using the distance formula which is derived from the Pythagorean theorem. The formula is √((x2-x1)^2 + (y2-y1)^2), where (x1, y1) and (x2, y2) are the coordinates of the two points.

Let's apply this formula to the points given:

1. x1 = 4, y1 = -2
2. x2 = -6, y2 = 4

Now plug these into the formula:

√((-6-4)^2 + (4-(-2))^2)
= √((-10)^2 + (6)^2)
= √(100 + 36)
= √136
= √(4∙ 34)
= 2∙√34

So, the exact distance between the points is 2∙√34 units.

To find the precise distance between the points (4, -2) and (-6, 4), the distance formula, derived from the Pythagorean theorem, is employed. By substituting the coordinates into the formula, we calculate the distance as 2∙√34 units, providing an accurate measure based on mathematical principles and geometric relationships.