Question

Last question of the day!!

Answer 1

Correct options are 2, 5 and 7.

Explanation:

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

Distance formula:

`d=√((x_2-x_1)^2+(y_2-y_1)^2)`

Using distance formula, we get

`AB=√((-3-(-3))^2+(2-(-3))^2)`

`AB=√((0)^2+(5)^2)`

`AB=√(25)`

`AB=5`

Similarly,

`BC=√((1-(-3))^2+(2-2)^2)=4`

`AC=√((1-(-3))^2+(2-(-3))^2)=√(16+25)=√(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=(√(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.