Answer:
Part 1) Option A. 2
Part 2) Option B. 4
Step-by-step explanation:
we know that
The formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
step 1
Determine distance AC
we have
A(3,1),C(5,3)
substitute in the formula
[tex]d=\sqrt{(3-1)^{2}+(5-3)^{2}}[/tex]
[tex]d=\sqrt{(2)^{2}+(2)^{2}}[/tex]
[tex]d=\sqrt{8}\ units[/tex]
simplify
[tex]AC=2\sqrt{2}\ units[/tex]
therefore
The length AC is 2 square root of 2 units
step 2
Determine distance AE
we have
A(3,1),E(7,5)
substitute in the formula
[tex]d=\sqrt{(5-1)^{2}+(7-3)^{2}}[/tex]
[tex]d=\sqrt{(4)^{2}+(4)^{2}}[/tex]
[tex]d=\sqrt{32}\ units[/tex]
simplify
[tex]AE=4\sqrt{2}\ units[/tex]
therefore
The length AE is 4 square root of 2 units
