Question

What is the perimeter of triangle ABC ?

Answer 1

`9+√(41)`

Explanation:

From C-A, it goes from y=1 to y=5, so that 4 units

From A-B, it goes from x = -1 to x = 4, that is 5 units

Now, to find distance from B to C, we need to use the distance formula:

`D=√((y_2-y_1)^2+(x_2-x_1)^2)`

Where the variables are the respective points of B and C,

B (4,5) & C(-1,1)

So x_1 =4, y_1=5, x_2=-1, y_2=1

Plugging into the formula we get:

`D=√((y_2-y_1)^2+(x_2-x_1)^2)\\D=√((1-5)^2+(-1-4)^2)\\D=√(16+25)\\ D=√(41)`

Summing it all (perimeter is sum of 3 sides):

Distance =
`4+5+√(41)\\ =9+√(41)`

3rd answer choice is right.