Answer:
A. (-1, 3) (3, 2) (-2, 1)
B. [tex]\sqrt{17}[/tex] [tex]\sqrt{5}[/tex] [tex]\sqrt{26}[/tex]
Step-by-step explanation:
The formula for finding the midpoints is [tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex].
MIDPOINTS
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4-6}2,\frac{4+2 }2} )[/tex] = (-1, 3)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{4+2}2,\frac{4+0 }2} )[/tex] = (3, 2)
[tex](\frac{x_{1}+x_{2} }2}, \frac{y_{1}+y_{2} }2} )[/tex] = [tex](\frac{-6+2}2,\frac{2+0 }2} )[/tex] = (-2, 1)
Next, we will use the distance formula, [tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex].
DISTANCE
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1-3)^{2} + (3-2)^{2} }[/tex] = [tex]\sqrt{17}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(-1+2)^{2} + (3-1)^{2} }[/tex] = [tex]\sqrt{5}[/tex]
[tex]\sqrt{(x_{1}-x_{2})^{2} + (y_{1}-y_{2})^{2} }[/tex] = [tex]\sqrt{(3+2)^{2} + (2-1)^{2} }[/tex] = [tex]\sqrt{26}[/tex]
a. To find the coordinates of endpoints we must add two x values and divide by 2 and then add 2 y- values and divide by 2.
(4-6)/2=-1 (4+2)/2=3
Repeat for other sides.
(2-6)/2=-2 (2+0)/2=1
(2+4)/2=3 (4+0)/2=2
Coordinates of midpoints are (-1,3), (-2,1), (3,2)
b. Now we use the distance formula for each midpoint to find the length of the inner- triangle.
sqrt((-1+2)^2 + (3-1)^2)
Sqrt(5)
Repeat.
Sqrt(17)
Sqrt(26)
The lengths of the inner triangle are as follows:
(-1,3), (-2,1) = Sqrt(5)
(-1,3), (3,2) = Sqrt(17)
(-2,1), (3,2) = Sqrt(26)
