Question

In the coordinate plane, three vertices of a rectangle
PQRS are P(0,0), Q(0,b), and S(c,0). what are the coordinates of point R

Answer 1

You mean "rectangle" rather than "triangle", don't you ?

Answer 2

Yeah I meant to say rectangle

Answer 3

make a plot of it


q r

p s



q0 b rx y what corresponds to x and y ?

p0 0 sc 0

Answer 4

Since PQRS is a rectangle then :
\[\overrightarrow{SR}=\overrightarrow{PQ}\]
So :
\[\begin{pmatrix}x_R-x_S\\y_R-y_S\end{pmatrix}=\begin{pmatrix}x_Q-x_P\\y_Q-y_P\end{pmatrix}\]
So :
\[\begin{pmatrix}x_R-c\\y_R-0\end{pmatrix}=\begin{pmatrix}b-0\\0-0\end{pmatrix}\]
So :
\[x_R=b+c
\\y_R=0
\]

Answer 5

your calculations appear to be off, or im misreading your end results

Answer 6

R: (b+c, 0) ??

Answer 7

I got (c,b) as the answer

Answer 8

so did i :)

Answer 9

I have done a mistake, but the method it what is more important :

Answer 10

if we consider these are parallel lines, the vector stuff would turn out as:

from P to Q applied at P

x = 0 + t(0)
y = 0 + t(b)


from S to R is the same vector applied at S

xr = c + t(0)
yr = 0 + t(b)

by letting t represent the length of 1 vector, a unit length: t = 1

xr = c + 0
yr = 0 + b

Answer 11

thankyou

Answer 12

youre welcome, if you dont need to run vectors for this, id just go with the basic general plot construction