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Chapter 1: Problem 56

Determine whether the statement is true or false. Justify your answer. The points \((-8,4),(2,11),\) and \((-5,1)\) represent the vertices of an isosceles triangle.

Short Answer

Expert verified
Yes, the statement is true. The points (-8,4), (2,11), and (-5,1) represent the vertices of an isosceles triangle.

Step by step solution

01

Calculate the distances between the points

First, Calculate the distances between the points using the formula for distance between two points, which is \(d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}\) - Distance between (-8,4) and (2,11): \(d1 = \sqrt{(2 - (-8))^2 + (11 - 4)^2} = \sqrt{100 + 49} = \sqrt{149}\)- Distance between (-8,4) and (-5,1): \(d2 = \sqrt{(( -5)- (-8))^2 + (1 - 4)^2} = \sqrt{9 + 9} = \sqrt{18}\)- Distance between (2,11) and (-5,1): \(d3 = \sqrt{(( -5) -2)^2 + (1 - 11)^2} = \sqrt{49 + 100} = \sqrt{149}\)
02

Compare the calculated distances

Compare the calculated distances. We found that d1 = d3. Hence these points represent the vertices of an isosceles triangle because two sides have the same length.

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