Question

The upper-left coordinates on a rectangle are (-1, 4), and the upper-right coordinates are (3, 4). The rectangle has a perimeter of 24 units. Draw The rectangle on the coordinate plane below.

Answer 1

Answer:

Please refer to the attached diagram for answer.

Step-by-step explanation:

Upper-left coordinates on a rectangle are (-1, 4)

Upper-right coordinates are (3, 4)

Perimeter of rectangle = 24 units

To find:

To draw the rectangle on the coordinate plane.

Solution:

Let the rectangle be ABCD.

So, sides AB  = CD and BC = DA

Let Point A has coordinates (-1, 4).

And upper right coordinates will be adjacent to A.

So, let Point B (3, 4).

Let us find the distance between A and B by distance formula:

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

Where,

$x_2 = 3\\x_1 = -1\\y_2 = 4\\y_1 = 4$

$AB = \sqrt{(3-(-1))^2+(4-4)^2}\\\Rightarrow AB = \sqrt{(4)^2+(0)^2}\\\Rightarrow AB = 4$

AB = 4 = CD

Perimeter of rectangle = Sum of all four sides = 2 (AB+DA) = 24

$2 \times 4 + 2DA = 24\\\Rightarrow 2DA=24-8\\\Rightarrow 2DA=16\\\Rightarrow DA =8\ units$

As it is a rectangle, its adjacent sides will be perpendicular to each other.

When we move from A to B only x coordinate is changing and it has changed by  4 (3- (-1) ) units. (Found by subtracting the x coordinates of the two points.)

Similarly, when we will move from D to A, only y coordinate will change by 8 units. (D is lower left coordinate so add 8 to y)

$\Rightarrow y + 8 = 4 \Rightarrow y =-4$

$x$ coordinate will be same as that of A i.e. -1.

So, D will be (-1, -4)

Similarly, when we will move from C to B, only y coordinate will change by 8 units. (C is lower right coordinate so add 8 to y)

$\Rightarrow y + 8 = 4 \Rightarrow y =-4$

$x$ coordinate will be same as that of B i.e. 3.

So, C will be (3, -4).

Now, let us draw

A(-1, 4)

B(3, 4)

C (3, -4)

D(-1, -4)

Please refer to the attached diagram for answer.