Coordinate Geometry: PQRS Parallelogram

Then youIn summary, the conversation discusses the calculation of the coordinate of point S in a parallelogram with given vertices. The speaker is unsure if their method is correct, but ultimately arrives at the correct answer. However, there is concern about the basic approach and assumptions made. A suggestion is given to find the slopes of all lines to determine the first pair of parallel sides.
  • #1
Taylor_1989
402
14
I would like someone to give this a quick check, I am really not sure if I am over thinking this question. I got the right ans, just would like a quick check of my method; big thanks in advance.

question: [itex]P(-1,5), Q(8,10), R(7,5) & S(x,y)[/itex] are the veritices of the parallelogram PQRS. Calculate the coordinate of S.

So all I did was workout the gradient of the line Q & R and applied that backwards from P, which gave the ans y=0 x=-2 which is correct, but I can't get rid of the feeling, that I have done something wrong but not sure what.

Is this the correct way to approach this type of question, seems a little basic to me which causes the concern.
 
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  • #2
Well, you are making the assumption that side QR is parallel to side PS- that is, that the vertices are given "cyclicly" which is the standard way and apparently happens to be true. but still an assumption. What you could have done was find the slopes of all the lines given by P, Q, and R to find the first pair of parallel sides.
 

Related to Coordinate Geometry: PQRS Parallelogram

1. What is a parallelogram in coordinate geometry?

A parallelogram is a four-sided polygon with opposite sides that are parallel and equal in length. In coordinate geometry, it can be defined as a quadrilateral with four vertices (points) that can be represented by ordered pairs of numbers, and its opposite sides have equal slopes.

2. How do you determine if a quadrilateral is a parallelogram in coordinate geometry?

In coordinate geometry, a quadrilateral is a parallelogram if and only if its opposite sides are parallel. This can be determined by calculating the slopes of all four sides and checking if the opposite sides have equal slopes. If the slopes are equal, then the quadrilateral is a parallelogram.

3. How do you find the perimeter of a parallelogram in coordinate geometry?

The perimeter of a parallelogram in coordinate geometry can be found by adding the lengths of all four sides. This can be done by calculating the distance between each pair of points using the distance formula, and then adding the four distances together.

4. Can a parallelogram have a slope of zero in coordinate geometry?

Yes, a parallelogram can have a slope of zero in coordinate geometry. This would mean that two opposite sides are horizontal and parallel to the x-axis.

5. How do you prove that a quadrilateral is a parallelogram in coordinate geometry?

To prove that a quadrilateral is a parallelogram in coordinate geometry, you can show that its opposite sides have equal slopes, or that its opposite sides are parallel and equal in length. Another way to prove it is by showing that the opposite angles are congruent, or that the diagonals bisect each other.

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