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Chapter 13: Q. 27 (page 527)

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

Short Answer

Expert verified

Triangle AMY is an isosceles triangle because AM=AY.

Step by step solution

01

Step-1 – Given

The given vertices are A鈭�3,4,M3,1,andY0,2

02

Step-2 – To determine

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

03

Step-3 – Proof

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

We will use the distance formula to show thatAM=AYAM=AY

Using the distance formula, the length AM is:

AM=3鈭�鈭�32+1鈭�42AM=3+32+鈭�32AM=62+鈭�32AM=36+9AM=45

And, the length AY is:

AY=0鈭�鈭�32+鈭�2鈭�42AY=0+32+鈭�2鈭�42AY=32+鈭�62AY=9+36AY=45

Hence, we have shown thatAM=AY and that means the triangle AMY is an isosceles triangle.

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