Answer:
2) Option 9.4 is correct
Therefore the length of the given line segment is [tex]s=9.4[/tex] units
3) Option (1,1) is correct
Therefore the midpoint of the given line segment is M=(1,1)
Step-by-step explanation:
2) Given that the line segment CD with endpoints C at (-3,1) and endpoint at D (5,6)
To find the length of the given line segment :
That is to find the distance of the end points using distance formula
[tex]s=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex] units
Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-3,1) and (5,6) respectively
Substitute the points in the distance formula we have
[tex]s=\sqrt{(5-(-3))^2+(6-1)^2}[/tex] units
[tex]=\sqrt{(5+3)^2+(5)^2}[/tex] units
[tex]=\sqrt{8^2+5^2}[/tex]
[tex]=\sqrt{64+25}[/tex]
[tex]=\sqrt{89}[/tex]
[tex]=9.4[/tex]
Therefore [tex]s=9.4[/tex] units
Option 9.4 is correct
Therefore the length of the given line segment is [tex]s=9.4[/tex] units
3) Given that the line segment PG with point P at (-6,4) and point at G (8,-2)
To find the midpoint of the given line segment :
Midpoint formula is [tex]M=(\frac{x_1+x_2}{2},\frac{y_1+y_2}{2})[/tex]
Let [tex](x_1,y_1)[/tex] and [tex](x_2,y_2)[/tex] be the given points (-6,4) and (8,-2) respectively
Substituting the points in the midpoint formula we get
[tex]M=(\frac{-6+8}{2},\frac{4-2}{2})[/tex]
[tex]=(\frac{2}{2}+\frac{2}{2})[/tex]
[tex]=(1,1)[/tex]
Therefore M=(1,1)
Therefore option (1,1) is correct
Therefore the midpoint of the given line segment is (1,1)
