Chapter 13: Q. 27 (page 527)

Show that the triangle with vertices $A (- 3, 4), M (3, 1), and Y (0, 2)$ is an isosceles triangle.

Short Answer

Expert verified

Triangle AMY is an isosceles triangle because $A M = A Y$ .

Step by step solution

Step-1 – Given

The given vertices are $A (- 3, 4), M (3, 1), and Y (0, 2)$

Step-2 – To determine

We have to show that the triangle is an isosceles triangle.

Step-3 – Proof

An isosceles triangle is a triangle with two sides of equal length.

We will use the distance formula to show that $A M = A Y$ $A M = A Y$

Using the distance formula, the length AM is:

$\begin{array}{l} A M = \sqrt{{(3 - (- 3))}^{2} + {(1 - 4)}^{2}} \\ A M = \sqrt{{(3 + 3)}^{2} + {(- 3)}^{2}} \\ A M = \sqrt{{(6)}^{2} + {(- 3)}^{2}} \\ A M = \sqrt{36 + 9} \\ A M = \sqrt{45} \end{array}$

And, the length AY is:

$\begin{array}{l} A Y = \sqrt{{(0 - (- 3))}^{2} + {(- 2 - 4)}^{2}} \\ A Y = \sqrt{{(0 + 3)}^{2} + {(- 2 - 4)}^{2}} \\ A Y = \sqrt{{(3)}^{2} + {(- 6)}^{2}} \\ A Y = \sqrt{9 + 36} \\ A Y = \sqrt{45} \end{array}$

Hence, we have shown that $A M = A Y$ and that means the triangle AMY is an isosceles triangle.

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Show that the triangle with vertices $A (- 3, 4), M (3, 1), and Y (0, 2)$ is an isosceles triangle.

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Proof

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Show that the triangle with verticesA−3,4,M3,1,andY0,2is an isosceles triangle.

Short Answer

Step by step solution

Step-1 – Given

Step-2 – To determine

Step-3 – Proof

One App. One Place for Learning.

Most popular questions from this chapter

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Show that the triangle with vertices $A (- 3, 4), M (3, 1), and Y (0, 2)$ is an isosceles triangle.