2. what is the value of x? Show your work

The coordinates of the vertices of a polygon are (-2, 1). (-3, 3), (-1, 5), (2, 4), and (2, 1). What is the perimeter of the pol

kobusy [5.1K]

Answer:

$15.2\ units$

Step-by-step explanation:

step 1

Plot the vertices of the polygon to better understand the problem

we have

$A(-2, 1). B(-3, 3), C(-1, 5), D(2, 4),E(2, 1)$

using a graphing tool

The polygon is a pentagon (the number of sides is 5)

see the attached figure

The perimeter is equal to

$P=AB+BC+CD+DE+AE$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

step 2

Find the distance AB

$A(-2, 1). B(-3, 3)$

substitute in the formula

$d=\sqrt{(3-1)^{2}+(-3+2)^{2}}$

$d=\sqrt{(2)^{2}+(-1)^{2}}$

$d_A_B=\sqrt{5}=2.24\ units$

step 3

Find the distance BC

$B(-3, 3), C(-1, 5)$

substitute in the formula

$d=\sqrt{(5-3)^{2}+(-1+3)^{2}}$

$d=\sqrt{(2)^{2}+(2)^{2}}$

$d_B_C=\sqrt{8}=2.83\ units$

step 4

Find the distance CD

$C(-1, 5), D(2, 4)$

substitute in the formula

$d=\sqrt{(4-5)^{2}+(2+1)^{2}}$

$d=\sqrt{(-1)^{2}+(3)^{2}}$

$d_C_D=\sqrt{10}=3.16\ units$

step 5

Find the distance DE

$D(2, 4),E(2, 1)$

substitute in the formula

$d=\sqrt{(1-4)^{2}+(2-2)^{2}}$

$d=\sqrt{(-3)^{2}+(0)^{2}}$

$d_D_E=\sqrt{9}\ units$

$d_D_E=3\ units$

step 6

Find the distance AE

$A(-2, 1).E(2, 1)$

substitute in the formula

$d=\sqrt{(1-1)^{2}+(2+2)^{2}}$

$d=\sqrt{(0)^{2}+(4)^{2}}$

$d_A_E=\sqrt{16}\ units$

$d_A_E=4\ units$

step 7

Find the perimeter

$P=AB+BC+CD+DE+AE$

substitute the values

$P=2.24+2.83+3.16+3+4=15.23\ units$

Round to the nearest tenth of a unit

$P=15.2\ units$

6 0

2 years ago

What is an equation of the line that passes through the point (-5, -6) and is

Vikentia [17]

Answer: y= 2x +4

Step-by-step explanation:

1. To be able to write the equation of the line, you want to be able to find the slope first. To do so, rearrange the given equation x+2y=2 into slope-intercept form, which is y=mx+b

First subtract x from both side, which will give us 2y=2-x. Rearrange this to get 2y= -x+2. Then, divide both sides by 2. This will give us y= -1/2x+1

2. Now that you have the equation, look for the slope in the new equation; this will be the m value. In this case, the slope is -1/2. Since we are looking for a line that is perpendicular, we have to change the slope so that it is the opposite reciprocal. The opposite reciprocal of -1/2 is 2, so the slope of the equation we want to find is 2.

3. Next, all we have to do is plug the given ordered pair (-5, -6) and the slope that we found (m=2) into the point-slope equation, which is $y-y_{1} = m(x-x_{1} )$