Question

The length of a rectangle is shown below: On a coordinate grid from negative 6 to positive 6 on the x-axis and on the y-axis, two points A and B are shown. The point A is on ordered pair negative 2, 3, and the point B is on ordered pair 3, 3. If the area of the rectangle to be drawn is 30 square units, where should points C and D be located, if they lie vertically below A and B, to make this rectangle?

Answer 1

C = (3, -3), D = (-2, -3)

Explanation:

The distance between two points
`(x_1,y_1)\ and\ (x_2,y_2)` on the coordinate plane is given by:

`Distance=√((x_2-x_1)^2+(y_2-y_1)^2)`

Points ABCD form a rectangle with an area of 30 unit². Points A and B are located at A(-2, 3) and B(3, 3). The distance between A and B is:

`|AB|=√((3-(-2))^2+(3-3)^2)=5\ units`

|AB| = width = 5 units

Area of ABCD = |AB| * |BC|

30 = 5 * |BC|

|BC| = length = 6 units

Let point C be located at (c, d). Since point C is below point B, hence the c coordinate of point B would be the same as that of C. Hence C = (3, d)

`|BC|=√((3-3)^2+(d-3)^2) \\\\√(0+(d-3)^2)=6\\\\square\ both\ sides:\\\\(d-3) ^2=36\\\\take\ square\ root\ of\ both\ sides:\\\\d-3=\pm 6\\\\d=6+3\ or\ d=-6+3\\\\d=9\ or\ d=-3\\\\`

Since point C is vertically below point B, hence the y coordinate would be negative

d = -3

C = (3, -3)

Point D would have the same y coordinate as point C since they are on the same horizontal line. Also, point D would have the same x coordinate as point A since it is vertically below point A. Hence:

D = (-2, -3)