Good evening. I have a math problem that I need if someone can please check to see if I have correct and I will post each one separate.
Given directed line segment CD, if point E divides CD three-fourths of the way from C to D, find the coordinates of E, then plot E
C=(1, 6)
D=(-3, -4)
I used the partitioning segment equation and I worked it out below:
1 + 3/4 (-3 - 1)
1 + 3/4 (-4)
1 + -12/4
1 + -3=-2
X=-2
6 + 3/4 (-4 - 6)
6 3/4 (-10)
6 + -30/4
6/1 + -15/2 = 12/2 + -15/2=-3/2
Y= -1.5
Are these the correct answers?
looks good
Hello. I truly appreciate you checking this. I am a bit new to Geometry so trying to find my answers and work them out and then post.
Thank you
To find the coordinates of point E, you correctly used the partitioning segment equation. However, there seems to be a mistake in your calculations.
To find the x-coordinate of E, you correctly used the equation:
X = 1 + 3/4 (-3 - 1)
X = 1 + 3/4 (-4)
X = 1 + -12/4
X = 1 - 3
X = -2
So, the x-coordinate of E is -2.
To find the y-coordinate of E, you correctly used the equation:
Y = 6 + 3/4 (-4 - 6)
Y = 6 + 3/4 (-10)
Y = 6 + -30/4
Y = 6 - 15/2
Y = 12/2 - 15/2
Y = -3/2
So, the y-coordinate of E is -3/2 or -1.5.
Therefore, the correct coordinates of point E are (-2, -1.5).
To check if your answers are correct, let's use the given information and equations to find the coordinates of point E.
Using the partitioning segment equation, the x-coordinate of point E can be found by evaluating the formula: X = x1 + (3/4)(x2 - x1), where x1 and x2 are the x-coordinates of points C and D, respectively.
In this case, C = (1, 6) with x1 = 1, and D = (-3, -4) with x2 = -3.
Plugging these values into the equation X = 1 + (3/4)(-3 - 1), we get:
X = 1 + (3/4)(-4)
X = 1 + (-12/4)
X = 1 - 3
X = -2
Therefore, the x-coordinate of point E is -2.
Similarly, we can find the y-coordinate of point E using the equation: Y = y1 + (3/4)(y2 - y1), where y1 and y2 are the y-coordinates of points C and D, respectively.
Plugging in the values, we have y1 = 6 and y2 = -4.
Thus, Y = 6 + (3/4)(-4 - 6)
Y = 6 + (3/4)(-10)
Y = 6 + (-30/4)
Y = 6 - (15/2)
Y = 12/2 - 15/2
Y = -3/2
Therefore, the y-coordinate of point E is -3/2 or -1.5.
Based on your calculations, the coordinates of point E are indeed X = -2 and Y = -1.5, so your answers are correct.