Two sides of triangle CDE are 9 and 4, as shown. Write an equation in standard form for the line CD. Leave values as radicals.
There is a picture of a triangle that passes through point (4,0)
The answer is 65^1/2x + 4y = 4(65^1/2)
But, I don't understand how to do this problem.
You will have to give a better description of the diagram.
Here's a quick sketch I made in paint.
i49 . tinypic . com/2jhy0p . jpg
Remove the spaces. Also, Point E is on the origin.
your diagram is a contradiction.
you show angle E as 90º and sides 4,5, and 9
but 4^2 + 5^2 is not equal to 9^2.
I assume D is the given point (4,0).
Point C cannot be on the y-axis as you have shown.
To write the equation of the line CD in standard form, we need to find its slope and y-intercept. The given information states that two sides of triangle CDE are 9 and 4. However, we don't have enough information to determine which side of the triangle is represented by line CD.
Nevertheless, since we know that the line passes through the point (4,0), we can use that information to find the equation.
First, let's assume that the 4-unit side of the triangle is represented by line CD. In this case, we can determine the slope of line CD as the change in y divided by the change in x. Since the line passes through the point (4,0), we can use the coordinates to calculate the slope:
slope = (y2 - y1) / (x2 - x1)
slope = (0 - 0) / (4 - 4)
slope = 0 / 0
Since the result is undefined, it means that the assumed 4-unit side is a vertical line parallel to the y-axis. The equation of a vertical line parallel to the y-axis is in the form x = k, where k is the x-coordinate of any point on the line. In this case, the x-coordinate of any point on line CD would be 4.
Thus, the equation of line CD, if the 4-unit side is represented by line CD, is x = 4.
Now, let's assume that the 9-unit side is represented by line CD. In this case, we can determine the slope of line CD as:
slope = (y2 - y1) / (x2 - x1)
slope = (0 - 0) / (4 - 9)
slope = 0 / -5
slope = 0
Since the slope is 0, it means that the assumed 9-unit side is a horizontal line parallel to the x-axis. The equation of a horizontal line parallel to the x-axis is in the form y = k, where k is the y-coordinate of any point on the line. In this case, the y-coordinate of any point on line CD would be 0.
Thus, the equation of line CD, if the 9-unit side is represented by line CD, is y = 0.
Therefore, we have two possible equations for line CD:
If the 4-unit side is represented by line CD: x = 4
If the 9-unit side is represented by line CD: y = 0
Without additional information specifying which side is represented by line CD, we cannot determine a single equation in standard form.