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Butoxors [25]
3 years ago
5

The coordinates of ∆ABC are A(-3, 2), B(5, 8) & C(11, 0). Which type of triangle is ∆ABC? Select All that apply.

Mathematics
1 answer:
stepan [7]3 years ago
7 0

Given:

The coordinates of ∆ABC are A(-3, 2), B(5, 8) & C(11, 0).

To find:

The type of the given triangle.

Solution:

Distance formula:

D=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}

Using the distance formula, we get

AB=\sqrt{(5-(-3))^2+(8-2)^2}

AB=\sqrt{(8)^2+(6)^2}

AB=\sqrt{64+36}

AB=\sqrt{100}

AB=10

Similarly,

BC=\sqrt{(11-5)^2+(0-8)^2}

BC=\sqrt{(6)^2+(8)^2}

BC=\sqrt{36+64}

BC=\sqrt{100}

BC=10

And,

AC=\sqrt{(11-(-3))^2+(0-2)^2}

AC=\sqrt{(14)^2+(-2)^2}

AC=\sqrt{196+4}

AC=\sqrt{200}

AC=10\sqrt{2}

Two sides of the triangle are equal, i.e., AB=BC. So, the triangle is an isosceles triangle.

Sum of square of two smaller side is

AB^2+BC^2=10^2+10^2

AB^2+BC^2=100+100

AB^2+BC^2=200

AB^2+BC^2=AC^2

Using the Pythagoras theorem, we can say that the given triangle is a right triangle.

Therefore, the correct options are B and F.

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