Four points or drawn on the coordinate plane and connected with straight lines to form a rectangle. three of the vertices of the rectangle or located at (2,1), (2,4), and (-4,4)

Question:

Four points are drawn on the coordinate plane and connected with straight lines to form a rectangle. Three of the vertices of the rectangle are located at (2, 1), (2, 4), and (-4, 4).

a.What are the coordinates of the fourth vertex of the rectangle?

b.What are the dimensions of the rectangle?

c.What is the area of the rectangle?

A)the coordinates of the fourth vertex of the rectangle is (-4,1)

B)The dimension of the rectangle is 6 by 3

C) The area of the rectangle  is 18 square units

Step-by-step explanation:

A)The coordinates of the fourth vertex of the rectangle

let (2, 1) be point A, (2, 4) be point B and (-4, 4)be point D.

we can see that A and B have the same x value i.e 2, and it is most likely that this rectangle is not slanted as B and C have the same y value.

From point B to point A, the y value decreased by 3, so we can say that from point C to point D the y value should also decreased by 3 units. We can therefore deduce that the y value of D=(4+3)=1. Now for the x values...

From point B to point D the x value decreased by 6, so we can say that the x value should also decrease by 6 from point A to point D... Therefore the x value of D is (2-6)= -4 (Which is the same x value as point C)

The coordinate is (-4,1)

B) The dimensions of the rectangle

We can find the dimensions that is the length and trhe breadth with the coordinates

Let the width of the rectangle be x

then x =

x=

x=

x=

x=3 units

Let the length of the rectangle be y

y=

y=

y=

y=

y=6 units

C) The area of the rectangle

The are of the rectangle is the product of it6s length and width

Area =

Area =

Area =  18 square units

step-by-step explanation:

i think something is missing in your question because y-1=(x-12) would not pass through the point (-4,-3). because if you replace x by -4 your are supposed to find y=-3 which is not the case her. if you replace x by -4 you find =-15.

i assume the right equation is y-1=1/4*(x-12) because this one is passing through both your points (if you are interested to know how i found that out i can tell you).

in this equation if i replace x by -4 i find y=-3 and if i replace x by 12, i find y=1 so the line representing this equation is passing through those 2 points.

then the standard form of the equation is finding an expression of y in function of x

y-1=1/4*(x-12)

y=x/4-3+1

y=x/4-2

hope that .

do you confirm there was a mistake in the question?