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On your paper, construct a rectangle on a coordinate plane that satisfies these criteria.

german

Answer:

$A = (5,3)$

$B = (-5,3)$

$C = (-5,-8)$

$D = (5,-8)$

Step-by-step explanation:

Required

$Perimeter = 42$

Construct a rectangle whose perimeter is 42 units and satisfies the given conditions.

First, name the rectangle ABCD.

Such that:

$A = (x_1,y_1)$

$B = (x_2,y_2)$

$C = (x_3,y_3)$

$D = (x_4,y_4)$

For the rectangle to be either horizontal or vertical, then:

$y_1 = y_2$ and $y_3 = y_4$

We have that:

$Perimeter = 42$

Replace perimeter with its formula

$2(AB + BC) = 42$

Divide both sides by 2

$AB + BC = 21$

This implies that, the distance between adjacent sides (through the edges) must be equal to 21

Having said that: a set of coordinates that satisfy the given conditions are:

$A = (5,3)$ -- First quadrant

$B = (-5,3)$ -- Second quadrant

$C = (-5,-8)$ -- Third quadrant

$D = (5,-8)$ -- Fourth quadrant

The above quadrants satisfy the condition:

$y_1 = y_2$ and $y_3 = y_4$

HOW TO KNOW THE PERIMETER IS 42

To do this, we simply calculate the distance between the edges and add them up

Distance is calculated as:

$D = \sqrt{(x_1 - x_2)^2 + (y_1 - y_2)^2$

For AB

$A = (5,3)$

$B = (-5,3)$

$D_1 = \sqrt{(5 - (-5))^2 + (3 - 3)^2}= \sqrt{(10)^2 + (0)^2} = \sqrt{100} = 10$

For BC

$B = (-5,3)$

$C = (-5,-8)$

$D_2 = \sqrt{(-5 - (-5))^2 + (3 - (-8))^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11$

For CD

$C = (-5,-8)$

$D = (5,-8)$

$D_3 = \sqrt{(-5 -5)^2 + (-8 - (-8))^2}= \sqrt{(-10)^2 + (0)^2} = \sqrt{100} = 10$

For DA

$D = (5,-8)$

$A = (5,3)$

$D_4 = \sqrt{(5 -5)^2 + (-8 -3)^2}= \sqrt{(0)^2 + (11)^2} = \sqrt{121} = 11$

So, the perimeter is:

$P = D_1 + D_2 + D_3 + D_4$

$P = 10 + 11 + 10 +11$

$P = 42$

See attachment for rectangle

8 0

3 years ago

A cone has a base radius of 2 millimeters and a height of 24 millimeters.

pishuonlain [190]

The answer is D. 32? mm3. The volume of the cone is: V = 1/3 * π * r^2 * h, where r is the radius and h is the height. We know that: r = 2 mm and h = 24 mm. Therefore, the volume of the cone is: V = 1/3 * π * r^2 * h = 1/3 * π * 2^2 * 24 = 1/3 * π * 4 * 24 = 1/3 * π * 96 = 32 π mm^3.

3 0

3 years ago

Before the trip, Tyler read 24 pages of his Philadelphia guidebook in an hour. The guidebook is 84 pages long. If he continued t

Tom [10]

Answer:

3 1/2 hours

Step-by-step explanation:

84/24 = 3.5

5 0

3 years ago

what is the measure of the vertex angle of an isosceles triangle i’d one of its base angles measures 42°

Naya [18.7K]

The measure of the vertex angle of the isosceles Δ is 96°

Step-by-step explanation:

In the isosceles triangle

Two sides are equal in lengths
The angle between the two equal sides is called vertex angle
The other two angles are called base angles
The base angles are equal in measure

∵ The measure of one of the base angles of an isosceles Δ = 42°

- The base angles are equal in measure

∴ The measure of the other base angle = 42°

∵ The sum of the measures of the interior angles of any Δ = 180°

∴ 42 + 42 + measure of the vertex angle = 180

∴ 84 + measure of the vertex angle = 180

- Subtract 84 from both sides

∴ measure of the vertex angle = 96°

The measure of the vertex angle of the isosceles Δ is 96°

Learn more:

You can learn more about the triangles in brainly.com/question/6530759

#LearnwithBrainly

8 0

3 years ago

15+6x=45+8x what does x equal

wel

Answer:

X=-15

Step-by-step explanation:

Do simple math

6 0

4 years ago

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