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

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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
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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)
 
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  • #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
 

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.

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