-gre.ge.11 x,y of fourth corner of diagonal

  • MHB
  • Thread starter karush
  • Start date
In summary, the conversation discusses finding the fourth vertex of a rectangle in a standard (x,y) coordinate plane. The options given are (3,-7), (4,-8), (5,-1), (8,-3), and (9,-3). The speaker uses the fact that the width of the rectangle is 3 and the height is 2 to determine that the fourth vertex is (3,-7). The conversation also mentions checking that the lines connecting the given vertices are not perpendicular to confirm that the shape is a rectangle.
  • #1
karush
Gold Member
MHB
3,269
5
In the standard (x,y) coordinate plane below, 3 of the vertices of a rectangle are shown. Which of the following is the 4th vertex of the rectangle?

boyce_20201004144618.png

sorry about the huge image but couldn't find where to scale it down
a. (3,-7)
b. (4,-8)
c. (5,-1)
d. (8,-3)
e. (9,-3)

ok I don't think we need a bunch of equations to do this
$\delta$ x of the with is 3
$\delta$ y of the width is 2

so the fourth corner is
(6-3,-5-2)=(3,-7)
 
Mathematics news on Phys.org
  • #2
I get that from (2, 1) to (6, -5) is a "delta" of (6- 2, -5- 1)= (4, -6). So the line parallel to that through (-1, -1) goes through (-1+ 4, -1- 6)= (3, -7) also.
 
  • #3
Just to cover all bases I'd first show that the lines (-1, -1) to (6, -5) and (2, 1) to (-1, -1) are not perpendicular so the line from (-1, -1) to (6, -5) must be a diagonal.

-Dan
 
  • #4
good point
by observation it sure looks like a rectangle
 

FAQ: -gre.ge.11 x,y of fourth corner of diagonal

1. What is the formula for finding the fourth corner of a diagonal?

The formula for finding the fourth corner of a diagonal is (x,y) = (x1 + x2 - x3, y1 + y2 - y3), where (x1,y1) and (x2,y2) are the coordinates of the two known corners of the diagonal and (x3,y3) is the coordinate of the third corner.

2. How do I determine which point is the third corner in the formula?

In order to determine which point is the third corner, you can use the Pythagorean theorem. The point with the longest distance from the other two points will be the third corner.

3. Can I use this formula for any shape?

No, this formula is specifically for finding the fourth corner of a diagonal in a rectangle or square. It may not work for other shapes.

4. What if I only have the length and width of the rectangle, can I still use this formula?

Yes, you can still use this formula if you only have the length and width of the rectangle. Simply plug in the values for (x1,y1) and (x2,y2) as (0,0) and (length, width) respectively.

5. Is there a way to check if my answer is correct?

Yes, you can use the distance formula to check if your answer is correct. The distance between the two known corners should be the same as the distance between the fourth corner and one of the known corners.

Similar threads

MHB -gre.ge.04 intersection of parabola and line
Replies
5
Views
1K
MHB What is the Relationship Between X and Y in these Mathematical Sequences?
Replies
4
Views
1K
Obtain the digits ## x ## and ## y ##
Replies
3
Views
995
MHB Divanshu's question via email about cylindrical shells
Replies
1
Views
4K
MHB Pre-calculus Grade 11 IB (higher level)
Replies
2
Views
2K
MHB Win a $10 or $5 Prize in Tom's 4/19 Lottery Fundraiser
Replies
1
Views
2K
I Can New Theorems Predict Incomplete 5x5 Magic Square Solutions?
2
Replies
68
Views
10K
MHB Mason's question via Facebook about solving a system of equations (2)
Replies
1
Views
10K
MHB Displacement-Time Graph Velocity of Objects X & Y
Replies
1
Views
1K
MHB Brenton's questions via email about volume by revolution
Replies
1
Views
4K

Hot Threads

Recent Insights

Back
Top