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Anettt [7]
3 years ago
6

Last question of the day!!

Mathematics
1 answer:
erma4kov [3.2K]3 years ago
3 0

Answer:

Correct options are 2, 5 and 7.

Step-by-step explanation:

Consider the given vertices of triangle are A(-3,-3), B(-3,2) and C(1,2).

Distance formula:

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

Using distance formula, we get

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

AB=\sqrt{(0)^2+(5)^2}

AB=\sqrt{25}

AB=5

Similarly,

BC=\sqrt{(1-(-3))^2+(2-2)^2}=4

AC=\sqrt{(1-(-3))^2+(2-(-3))^2}=\sqrt{16+25}=\sqrt{41}

From the above calculation it is clear that AC>AB and AC>BC.

According to Pythagoras theorem, in a right angle triangle, the square of largest side is equal to the sum of squares of two small sides.

hypotenuse^2=base^2+perpendicular^2

AC^2=(\sqrt{41})^2=41

AB^2+BC^2=(5)^2+4^2=24+16=41=AC^2

So, given triangle is a right angle triangle and AC is its hypotenuse.

Therefore, the correct options are 2, 5 and 7.

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