Question

The coordinates of two of the vertices of square QRST are shown.

Q (3.6,2.1)


R (¯5.4,2.1)

What is the length, in units, of each side of square QRST? Use the coordinates to show or explain how you determined the length.


Enter your answer and your work or explanation in the space provided.

Answer 1

Therefore the length of each side of square
`QRST` is
`9\ unit`.

Explanation:

Given that,

`QRST` is a square.

The coordinate of point
`Q` is
`(3.6,2.1)`.

The coordinate of point
`R` is
`(-5.4,2.1)`.

Let, The coordinate of point
`S` is
`(-5.4,y)` and the coordinate of point
`T` is
`(3.6,y)`.

Diagram of the square
`QRST` is shown below:

Now,

`QR=\sqrt{(-5.4-3.6)^(2) +(2.1-2.1)^(2) }` [Distance Formula]

`QR=\sqrt{(9)^(2) -(0)^(2) }`

`=√(81)`

`= 9\ unit`

Therefore the length of square
`QRST` is
`9\ unit.`

`RS=\sqrt{(-5.4+5.4)^(2) +(y-2.1)^(2) }`

`9=\sqrt{(0)^(2) +(y-2.1)^(2) }` [
`QR=RS`, because
`QRST` is a square]

⇒
`9=\sqrt{(y-2.1)^(2) }`

squaring both sides, we get

⇒
`81=(y-2.1)^(2)`

⇒
`(y-2.1)`
`=` ±
`9`

∴
`y=11.1`

The coordinate of point
`S` is
`(-5.4,11.1)` and the coordinate of point
`T` is
`(3.6,11.1)`.

∵
`QRST` is a square

∴
`QR=RS=ST=TQ=9\ unit`

Therefore the length of each side of square
`QRST` is
`9\ unit`.