Question

We can find the length of FG using the Distance Formula:

FG = (3 - 1)^2 + (-1 - 3)^2
Which formula also represents the length of FG?
A) FG = 4 + 2
B) FG = (4 + 2)^2
C) FG = (4 - 2)^2
D) FG^2 = 4^2 + 2^2

Answer 1

also, FG=(2)^2+(-4)^2
FG=4+16
FG=20
so see which ones end up with 20

not A
not B
not C
D is the answer

Answer 2

Answer: D.
`FG^2 = 4^2 + 2^2`

Explanation:

Given: We can find the length of FG using the Distance Formula:

[Distance formula to find length of line from point
`(x_1,y_1)` to point
`(x_2,y_2` is given by :-

`d=√((x_2-x_1)^2+(y_2-y_1)^2))\\\\\Rightarrow d^2=(x_2-x_1)^2+(y_2-y_1)^2`]

`FG^2 =(3 - 1)^2 + (-1 - 3)^2`

Since,
`3-1=2` and
`-1-3=-(1+3)=-4`

Therefore,
`FG^2 =(2)^2 + (-4)^2=2^2+((4)(-1))^2=2^2+4^2(-1)^2=2^2+4^2`

Hence, the formula also represents the length of FG is
`FG^2 = 4^2 + 2^2`.