Question 3 Determine the leg lengths between the two points: (6, -3) and (-2,4). what the shortest leg length?
and what is the the longest leg length?
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9

Step-by-step explanation:

→You can use the Pythagorean Theorem to solve this, by plugging in the numbers, like so:

\begin{gathered}a^2+b^2=c^2\\x^2+(x-3)^2=(x+3)^2\end{gathered}

a

2

+b

2

=c

2

x

2

+(x−3)

2

=(x+3)

2

x^2+x^2-6x+9=x^2+6x+9x

2

+x

2

−6x+9=x

2

+6x+9

→Subtract x^2-6x+9x

2

−6x+9 from both sides:

x^2 = 12xx

2

=12x

→Subtract 12x from both sides:

x^2 -12x=0x

2

−12x=0

→Factor out x:

x(x-12)=0x(x−12)=0

→Separate, set = to 0, and solve:

\begin{gathered}x = 0\\x -12=0\end{gathered}

x=0

x−12=0

→ Add 12 to both sides: x = 12x=12

→So we have 0 and 12, as our answers. However, we cannot have 0 as a side length, since this would not be possible.

→All we need to do is take 12, and plug it into the equation for the shortest leg.

\begin{gathered}x - 3=?\\12-3=9\end{gathered}

x−3=?

12−3=9

(23*2)-12=x     x=34

step-by-step explanation: