Question

The coordinates of rectangle PQRS are P(1,6),Q(1,2),R(9,2) and S(9,6). Show that the diagonals are equal in length.

Answer 1

Hi :)

Answer 2

HI!(:

Answer 3

Diagonal SQ

Answer 4

So are they not of equal lengths?

Answer 5

They are indeed! ....you'll see :)

Answer 6

When I put that diagonal...it looks like we have a 2 separate right triangles right?

Answer 7

Right... So?

Answer 8

So thanks to the pythagorean theorem...we know that the hypotenuse (diagonal) is equal to

\[\large SQ = \sqrt{QR^2 + RS^2} \]

Answer 9

So what is the distance from point Q to point R ?

Answer 10

I'm so confused..

Answer 11

me too but hi :DD

Answer 12

urhm. Hi.

Answer 13

check how long is from P to R
and from Q to S

that is, check if their DISTANCE in between those points, the points for the diagonals
are the same

\(\bf \textit{distance between 2 points}\\ \quad \\
\begin{array}{lllll}
&x_1&y_1&x_2&y_2\\
P&({\color{red}{ 1}}\quad ,&{\color{blue}{ 6}})\quad R&({\color{red}{ 9}}\quad ,&{\color{blue}{ 2}})
\\ \quad \\
Q&({\color{red}{ 1}}\quad ,&{\color{blue}{ 2}})\quad S&({\color{red}{ 9}}\quad ,&{\color{blue}{ 6}})
\end{array}\qquad
d = \sqrt{({\color{red}{ x_2}}-{\color{red}{ x_1}})^2 + ({\color{blue}{ y_2}}-{\color{blue}{ y_1}})^2}\)

Answer 14

Wait, so you do the distance formula on PR then QS and thhheeeeennnnn... Compare them?