Question

[4] Prove that the points A(4,3), B(7,-1) and C(9,3) are the vertices of an isosceles triangle.​

Answer 1

Answer:

Step-by-step explanation:

An isosceles triangle is a triangle with (at least) two equal sides.

Formula: Distance between two points= √(x2–x1)² + (y2–y1)²

A = (4,3)   B = (7,−1)   C = (9,3)  

AB = √(7 - 4)² + (-1 -3)²

AB = √(3) ² + (-4)²  

AB = √9 + 16  

AB = √ 25

AB = 5  

Similarly,  

AC= √(9-4)² + (3-3)²  

AC = √(5)² + (0)²  

AC = √25

AC = 5  

Now, we find  

BC = √(9-7)² + (3+1)²

BC = √(2)² + (4)²

BC = √4+16  

BC = √20

BC = 2√5

From this, we conclude that two sides are equal and one is not equal to any  which satisfies the property of Isosceles Triangles.

Hence Proved

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Answer 2

Answer:

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