Finding co-ordinates in squares

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In summary, the conversation is about finding the coordinates of B and D in a square with vertices A(7,2) and C(1,4). The equation of diagonal BD is y=3x-9 and the midpoint of AC is (4,3). The method to find the coordinates involves using the fact that the product of the slopes of the diagonals is -1 and that the diagonals have the same midpoint and equal distances to each corner.
  • #1
bob4000
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urgent! finding co-ordinates in squares

A(7,2) and C(1,4) are vertices of a square ABCD.

equation BD is y=3x-9

midpoints AC: (4,3)

find the co-ordinates of B and D

i just don't understan how to get the co-ordinates, I've tried plotting a graph but to no avail. i found the midpoints and the equation listed above with relative ease but this part of the question just baffles me. if anyone could just explain the method of this kind of task, i will be able to answer the question. thank you.
 
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  • #2
It might help to use the fact that the product of the slopes of the diagonals is -1.
 
  • #3
i used tht to find the equation, but i don't see how that can help me with the co-ordinates?
 
  • #4
It's even easier than I thought. The diagonals have the same midpoint and the distances from the midpoint to each corner are all the same.
 
  • #5
i think i get it now. thanks alot
 

What is the purpose of finding coordinates in squares?

The purpose of finding coordinates in squares is to determine the exact location of a point within a two-dimensional grid. This can be useful in many fields such as mathematics, geography, and computer graphics.

How do you find coordinates in a square?

To find coordinates in a square, you need to identify the x-coordinate (horizontal value) and the y-coordinate (vertical value) of the point within the square. The x-coordinate is found by counting the number of squares from the left edge of the grid to the point, while the y-coordinate is found by counting the number of squares from the bottom edge of the grid to the point.

What is the format of coordinates in squares?

The format of coordinates in squares is (x, y), where x represents the horizontal value and y represents the vertical value. The coordinates are separated by a comma and can be positive, negative, or zero.

Can coordinates in squares be decimals?

Yes, coordinates in squares can be decimals. This is often the case when dealing with more precise measurements or when working with a smaller grid.

How are coordinates in squares used in real life?

Coordinates in squares are used in real life in many ways, such as navigation apps on smartphones, mapping out locations on a grid, and in computer graphics to plot shapes and objects. They are also commonly used in geometry and physics for calculating distances and angles.

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