Good morning. I have a Geometry math problem that I need if someone can please check on to make sure I am doing the problem correct and to please check my answer.
#7
Given segment DF with D(-1, 11) and F(-9 , -5), if E partitions DF such that the ratio of DE to DF is 5:8, find the coordinates of E.
-1 + 5/8 (-9 - -1)
-1 + 5/8 (-8)
-1 + -40/8
-1 + -5= -6
X= -6
11 + 5/8 ( -5 - 11)
11 + 5/8 ( -16)
11 + -80/8
11 + -10 = 1
Y=1
E= (-6, 1)
Is this correct?
You could have checked using the distance formula
If E is (-6,-1)
then DE = √(25 + 144) = 13
EF = √(9 + 16) = 5
Ratio of 13:5 ≠ 5:8
I do these in the following way:
Make a sketch, let your point E be (x,y)
then for the x:
(x- (-1))/(-9 - x) = 5/8
8x + 8 = -45 - 5x
13x = -53
x = -53/13
for the y:
(y-11)/(-5-y) = 5/8
8y - 88 = -25 - 5y
13y = 65
y = 5
Hello Reiny. Are you saying I got my answer wrong or right? What you did above is that just the distance formula?
Hello Reiny,
I think I see the mistake I made is with the ratio.
5:8
5/5 + 8=5/13
I should have used the fraction of 5/13
My answer now is as follows:
X=-53/13 or -4 1/13
Y=63/13 = 4 11/13
Should I change the fractions into mixed fractions when I get -53/13? or when I get 63/13?
How can you possibly graph those fractions on a graph if you had to?
Thank you
To solve this problem correctly, you need to use the concept of a ratio to find the coordinates of point E.
The ratio given is DE to DF, which is 5:8. This means that DE is 5 parts and DF is 8 parts.
To find the coordinates of E, you can use the following steps:
Step 1: Find the difference between the x-coordinates of D and F:
x-coordinate of F - x-coordinate of D: -9 - (-1) = -9 + 1 = -8
Step 2: Divide the difference found in step 1 by the sum of the two parts in the ratio (5 + 8):
x-coordinate of D + (5 / (5 + 8)) * difference found in step 1: -1 + (5 / (5+8)) * -8 = -1 + (5 / 13) * -8 = -1 - (40 / 13) ≈ -4.07
Step 3: Find the difference between the y-coordinates of D and F:
y-coordinate of F - y-coordinate of D: -5 - 11 = -16
Step 4: Divide the difference found in step 3 by the sum of the two parts in the ratio (5 + 8):
y-coordinate of D + (5 / (5 + 8)) * difference found in step 3: 11 + (5 / (5+8)) * -16 = 11 + (5 / 13) * -16 = 11 - (80 / 13) ≈ 4.15
Therefore, the coordinates of point E are approximately (-4.07, 4.15), which is different from (-6, 1) that you provided.
So, the correct answer is (-4.07, 4.15).