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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.

User Dzida
by
6.8k points

1 Answer

5 votes

Answer:

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.

The coordinates of two of the vertices of square QRST are shown. Q (3.6,2.1) R (¯5.4,2.1) What-example-1
User Roxrook
by
7.1k points