Just need a starting point: One side of rhombus is y=2x, two opposite vertices...

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Kitimbo

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One side of a rhombus is the line y=2x and two opposite vertices are the points (0,0) and (4½,4½).Find the equations of the diagonals and the coordinates of the other 2 sides.
 
Kitimbo said:
One side of a rhombus is the line y=2x and two opposite vertices are the points (0,0) and (4½,4½).Find the equations of the diagonals and the coordinates of the other 2 sides.
Click to expand...
Your starting point is to draw a nice clear diagram. It might also help to recall that the diagonals of a rhombus bisect at right angles.
 
Kitimbo said:
One side of a rhombus is the line y=2x and two opposite vertices are the points (0,0) and (4½,4½).Find the equations of the diagonals and the coordinates of the other 2 sides.
Click to expand...
The exercise ought to ask for the coordinates of the other two vertices. (It doesn't make sense to ask for the coordinates of a line segment.)

You already know that a rhombus has four sides of equal length.

You already drew a rough sketch, so you roughly know what this particular rhombus looks like.

One way to continue would be to use the Distance Formula, to find the point on the given line which is the same distance from (0,0) as it is from (4.5,4.5). In the formula, remember that you may replace y with 2x.

Can you show your work finding the point on the line which is equidistant from the two given points? :cool:
 
(4.5-0)²+4.5-0)²=(x-0)²+(y-0)²
40.5=x²+y²
So I got x=√8.1 after replacing y with 2x so I couldn't continue any more
 
Kitimbo said:
(4.5-0)²+4.5-0)²=(x-0)²+(y-0)²

This statement is saying that the distance from (0, 0) to (4.5, 4.5) is the same as (x, y) to (0, 0). Look at your diagram...that can't be right.

You want a statement to show that the distance from (0, 0) to (x, y) is the same as (x, y) to (4.5, 4.5). Can you see why? ....look at your diagram.

40.5=x²+y²
So I got x=√8.1 after replacing y with 2x so I couldn't continue any more
Click to expand...
.
 
What is this supposed to be? You have been told how to solve your problem. Please do that and show what you have done step by step so we can check it.
 
(x-0)²+(y-0)²=(4.5-x)²+(4.5-y)²
x²+y²=40.5-18x+2x²
The I replace y with 2x
3x²+18x-40.5=0
 
Kitimbo said:
(x-0)²+(y-0)²=(4.5-x)²+(4.5-y)²
x²+y²=40.5-18x+2x² ...............Incorrect
The I replace y with 2x
3x²+18x-40.5=0
Click to expand...

(x-0)²+(y-0)²=(4.5-x)²+(4.5-y)²

(x)²+(y)² = (20.25 - 9x + x²) + (20.25 - 9y + y²)

x²+y² = 40.5 - 9x + x² - 9y + y²

0 = 40.5 - 9x - 9y

Now continue.....
 
Thanks in advance, I got the first point (1.5,3) so I can find the others.
 
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