Answer:
(a)2.2 units
(b)(-2.5, 3)
Explanation:
From the diagram, the coordinates of A, B and C are:
A(-3,2), B(-2,4) and C(-1,3)
(a)To determine the length of AC, we use the distance formula.
[tex]Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex][tex](x_1,y_1)=A(-3,2$)and(x_2,y_2)=C(-1,3).$[/tex]
Therefore:
[tex]\begin{gathered} AC=\sqrt[]{(-1-(-3))^2+(3-2)^2} \\ =\sqrt[]{(-1+3)^2+(1)^2} \\ =\sqrt[]{2^2+1^2} \\ =\sqrt[]{5} \\ =2.2\text{ units} \end{gathered}[/tex]
The length of AC is 2.2 units
(b)The midpoint of a line segment is calculated using the formula:
[tex]Midpoint=\mleft(\dfrac{x_2+x_1}{2},\dfrac{y_2+y_1}{2}\mright)[/tex]
Given the coordinates of A and B as follows:
A(-3,2), B(-2,4)
The midpoint of AB is:
[tex]\begin{gathered} Midpoint=(\dfrac{-3_{}+(-2)}{2},\dfrac{2_{}+4}{2}) \\ =(-\frac{5}{2},\frac{6}{2}) \\ =(-2.5,3) \end{gathered}[/tex]
The midpoint of AB is (-2.5, 3).
