C(4,10) and D(3,5) which is CD is intersected by BE
B(-2,6).How to find E.
No way to tell from what you have here. All we know is that E is somewhere on CD.
You forgot to mention that we had A(-1,5) and that BE is parallel to AD.
Since the y-coordinate of B = 6, and 6 is 1/5 of the way from 5 to 10 (the y-coordinates of CD), the x-coordinate of E will be 1/5 of the way from 3 to 4. If this is confusing, you need to review the properties of parallel lines and transversals.
To determine if the line segment CD is intersected by line BE, we can use the method of finding the intersection point of two lines.
First, let's find the equations of the lines CD and BE.
The equation of a line can be represented in the slope-intercept form, y = mx + b, where m is the slope of the line and b is the y-intercept.
Let's find the equation of line CD using the points C(4, 10) and D(3, 5):
1. Find the slope (m) of line CD:
m = (y₂ - y₁) / (x₂ - x₁)
= (5 - 10) / (3 - 4)
= -5
2. Use the slope-intercept form to find the equation of line CD:
y = mx + b
10 = -5(4) + b
10 = -20 + b
b = 30
Therefore, the equation of line CD is: y = -5x + 30.
Now, let's find the equation of line BE. Since we do not have the coordinates of points B and E, we need more information to continue the calculation. Please provide the coordinates of points B and E so that we can determine if line CD is intersected by line BE.