What is the distance between the points -2 -6 and 7-3?

Answer 1

According to the Pythagorean Theorem, the sum of the squares of the lengths of the two sides of a right triangle that are adjacent to (touching) the right angle is equal to the square of the length of the hypotenuse. Algebraically, a2 + b2 = c2, where c is the length of the hypotenuse and a and b are the lengths of the other two sides.

This might not make sense unless you follow along on graph paper: Imagine the line segment connecting (-2, -6) and (7, -3) as the hypotenuse of a right triangle, with one of the other sides parallel to the x axis and the third side parallel to the y axis. That would make the point at the right angle (7, -6) if the right angle is at the lower right or (-2, -3) if the right angle is at the upper left (it doesn't matter on which side of the hypotenuse you choose to make the triangle). The length of a, the segment connecting (-2, -6) and (7, -6) or the segment connecting (7, -3) and (-2, -3), is 9 [7 - (-2)], and the length of b, the segment connecting (-2, -6) and (-2, -3) or the segment connecting (7, -3) and (7, -6), is 3 [(-3) - (-6)]. So c2 = 92 + 32 = 81 + 9 = 90. Taking the square root of both sides of the equation, c, the distance you are looking for, is √90. Since 90 = 2 x 32 x 5, √90 can be simplified to 3√10, which is approximately 9.49.

Answer 2

Points: (7, 3) and (-2, 6)

Distance: 3 Times Square root of 10 or about 9.487 rounded up to 3 decimal places