# If two vertices of a square on the same side AB are A(1,2) and B(2,4)....

• Julian102
In summary, to find the other two vertices C and D of a square with side AB given vertices A(1,2) and B(2,4), you can use the equations 1-6 provided. First, compute the equation of the line AB using formula 4. Then, use formula 2 to find the slope of the line and formula 3 to find the slope of the perpendicular line. Next, use formula 1 to find the equations of lines AD and BC. From there, you can locate the points C and D on these lines using the distance formula. Alternatively, if you have studied vectors, you can use vector AB to find a perpendicular vector of the same length, which will also help you locate points
Julian102

## Homework Statement

If two vertex of a square of the side AB is A(1,2) and B(2,4) find other two vertex C and D?

## Homework Equations

1. y-y1 = m ( x-x1)
2. m=y1-y2 / x1-x2
3. m1*m2= -1
4. (x-x1) / (x1-x2) =(y-y1)/(y1-y2)
5. m=tanA
6. If ax+by+c=0 then its parallel line is ax+by+k=0

## The Attempt at a Solution

Equation of AB is can be found using formula 4 , then slope is found using formula 2 . Then slope of perpendicular is -1/m (formula 3) . Now perpendicular AD and BC can be found using formula 1 . Now CD is parallel to AB . I need to find CD ...The distance between AB and CD is root 5 (of course since distance between AB is root 5 and it is a square) ...Please tell me how to find the side CD ...and diagonals AC and BD ...

Julian102 said:

## Homework Statement

If two vertex of a square of the side AB is A(1,2) and B(2,4) find other two vertex C and D?

## Homework Equations

1. y-y1 = m ( x-x1)
2. m=y1-y2 / x1-x2
3. m1*m2= -1
4. (x-x1) / (x1-x2) =(y-y1)/(y1-y2)
5. m=tanA
6. If ax+by+c=0 then its parallel line is ax+by+k=0

## The Attempt at a Solution

Equation of AB is can be found using formula 4 , then slope is found using formula 2 . Then slope of perpendicular is -1/m (formula 3) . Now perpendicular AD and BC can be found using formula 1 . Now CD is parallel to AB . I need to find CD ...The distance between AB and CD is root 5 (of course since distance between AB is root 5 and it is a square) ...Please tell me how to find the side CD ...and diagonals AC and BD ...
Compute the equation of the line AB.
You can then easily write down the equations of the lines AD and BC (you gave the correct rules).
Then you can locate C and D (two possible solutions) on these lines using the distance.

Said differently: don't use words to describe a possible solution, just compute what you said.

Last edited:
Julian102
Alternatively, if you have studied vectors you don't need to deal with equations of straight lines and their slopes. Start with ##\vec{AB} = \langle 1,2\rangle##. Can you write down a perpendicular vector of the same length? That would get you started.

## 1. What are the coordinates of the other two vertices of the square?

The other two vertices of the square can be found by reflecting the given points A(1,2) and B(2,4) across the line AB. This will result in two new points, C(3,6) and D(4,8), which are the coordinates of the other two vertices of the square.

## 2. How do you know that the points A(1,2) and B(2,4) are on the same side of the square?

Since the given points A and B are on the same side of the square, they share a common side. This side will be perpendicular to the line connecting A and B, and its length will be equal to the distance between A and B. In this case, the distance between A(1,2) and B(2,4) is √5, which is also the length of the side of the square.

## 3. Can you determine the length of the square's side using only the given information?

Yes, the length of the square's side can be determined by finding the distance between the two given points A(1,2) and B(2,4). This can be done using the distance formula, which is √[(x2-x1)^2 + (y2-y1)^2]. In this case, the distance is √5, which is also the length of the side of the square.

## 4. Is it possible to find the area of the square with only two coordinates?

No, the area of a square cannot be determined with only two coordinates. In order to find the area, we need the length of at least one side of the square. In this case, since we have the length of the side, we can use the formula for the area of a square, which is side^2, to determine the area.

## 5. Can you use the given information to find the perimeter of the square?

Yes, the perimeter of the square can be found by adding the length of all four sides. Since we know the length of one side is √5, the perimeter can be calculated as 4*√5, which is approximately 8.94 units.

• Precalculus Mathematics Homework Help
Replies
4
Views
3K
• Precalculus Mathematics Homework Help
Replies
10
Views
16K
• General Math
Replies
1
Views
482
• General Math
Replies
2
Views
2K
• General Math
Replies
7
Views
2K
• Programming and Computer Science
Replies
2
Views
1K
• Precalculus Mathematics Homework Help
Replies
4
Views
3K
• Precalculus Mathematics Homework Help
Replies
3
Views
10K
• Precalculus Mathematics Homework Help
Replies
11
Views
7K
• Precalculus Mathematics Homework Help
Replies
5
Views
2K