Answer:
1. 18.81 units
2. 17.21 units
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{7.3 cm}\underline{Distance between two points}\\\\$d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$\\\\where $(x_1,y_1)$ and $(x_2,y_2)$ are the two points.\\\end{minipage}}[/tex]
Question 1
Given vertices of ΔABC:
- A = (-2, 3)
- B = (3, -3)
- C = (-2, -3)
Plot the vertices on the given graph paper and join with line segments to create the triangle.
As points B and C share the same y-coordinate:
[tex]\implies BC = |x_B-x_C|=|3-(-2)|=5\:\: \sf units[/tex]
As points A and C share the same x-coordinate:
[tex]\implies AC = |y_A-y_C|=|3-(-3)|=6\:\: \sf units[/tex]
Use the distance formula to find the length AB:
[tex]\begin{aligned}AB & =\sqrt{(x_B-x_A)^2+(y_B-y_A)^2}\\& =\sqrt{(3-(-2))^2+(-3-3)^2}\\& =\sqrt{(5)^2+(-6)^2}\\& =\sqrt{25+36}\\& =\sqrt{61}\\\end{aligned}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside.
[tex]\begin{aligned}\textsf{Perimeter of $ABC$} & = AB + BC + AC\\& = \sqrt{61}+5+6\\& = 11+\sqrt{61}\\& = 18.81\:\: \sf units\:(nearest\:hundredth)\end{aligned}[/tex]
Question 2
Given vertices of polygon KLMN:
- K = (-1, 1)
- L = (4, 1)
- M = (2, -2)
- N = (-3, -2)
Plot the vertices on the given graph paper and join with line segments to create the polygon.
As the y-coordinate of points K and L, and M and N are the same, KL and MN are parallel line segments.
As the difference between the x-coordinates of K and N, and L and M is 2 units, KN and LM are parallel line segments.
Therefore, the polygon is a parallelogram.
A parallelogram has two pairs of opposite sides that are equal in length.
Therefore, KL = NM and KN = LM.
As points K and L share the same y-coordinate:
[tex]\implies KL = |x_K-x_L|=|-1-4|=5\:\: \sf units[/tex]
Use the distance formula to find the length KN:
[tex]\begin{aligned}KN & =\sqrt{(x_N-x_K)^2+(y_N-y_K)^2}\\& =\sqrt{(-3-(-1))^2+(-2-1)^2}\\& =\sqrt{(-2)^2+(-3)^2}\\& =\sqrt{4+9}\\& =\sqrt{13}\\\end{aligned}[/tex]
The perimeter of a two-dimensional shape is the distance all the way around the outside.
[tex]\begin{aligned}\textsf{Perimeter of $KLMN$} & = 2\:KL + 2 \:KN\\& = 2 \cdot 5 + 2\cdot \sqrt{13}\\& =10 + 2\sqrt{13}\\& = 17.21\:\: \sf units\:(nearest\:hundredth)\end{aligned}[/tex]
