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1 . Triangle ABC has the following vertices: A (1,0) , B (5,0) and C (3,4) . which of the following is true ?

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Answer: Option B

Explanation:

Let's calculate the lengths of the sides of triangle ABC using the distance formula to determine which of the given options is true:

Distance Formula: The distance between two points (x1, y1) and (x2, y2) is given by √((x2 - x1)^2 + (y2 - y1)^2).

A (1, 0) and B (5, 0): AB = √((5 - 1)^2 + (0 - 0)^2) = √(4^2 + 0) = 4.

B (5, 0) and C (3, 4): BC = √((3 - 5)^2 + (4 - 0)^2) = √((-2)^2 + 4^2) = √(4 + 16) = √20.

A (1, 0) and C (3, 4): AC = √((3 - 1)^2 + (4 - 0)^2) = √(2^2 + 4^2) = √(4 + 16) = √20.

Now, let's compare the lengths:

AB = 4 BC = √20 AC = √20

From the calculations, it's clear that AC = BC, so the correct statement is:

CA = CB

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