Question

Elian is placing a rectangle in the coordinate plane. He knows that the shorter side of the rectangle is half the length of the longer side. He places the longer side on the x-axis. What coordinates should he assign to the top-left vertex of the rectangle? Enter your answer in the boxes. ( , )

A rectangle is in the coordinate plane so that the bottom left vertex is at 0 comma 0, the top left vertex is on the positive side of the y-axis and is labeled question mark comma question mark, the top right vertex is in the first quadrant, and the bottom right vertex is on the positive side of the x-axis and is labeled 2 a comma 0.

Answer 1

coordinates of top left vertex: (0, a)

Answer 2

(0, a)

Explanation:

We can start by imagining this rectangle as a square.

(This is written as if it is a square:)

The distance that a square reaches on the x-axis (assuming it has its lower left point at the origin, like this one does) is the same distance that it reaches on the y-axis.

meaning that we will have (length, 0) along the x-axis and (0, length) along the y-axis

so, if we are to treat this as a square, the point (2a, 0) means that our opposite vertex is (0, 2a)

However, because this length is only half of the length that it would be (if it were a square), we must divide our length by 2

2a ÷ 2 = a

So, the coordinates of the top-left vertex of this rectangle:

(0, a)