Good morning. I have another math problem I may have to have checked. I am not real good at re-checking with the distance formula.
#8
Given segment AB with A(8, -4) and B(-6, -11), if P partitions AB such that the ratio of AP to AB is 2:7, find the coordinates of P.
8+2/9 (-6 - -8)
8 + 2/9 (-14)
8+ -28/9
8/1 + -28/9= 72/9 + -28/9 =44/18=3
X=3
-4 + 2/9 ( -11 - -4)
-4 + 2/9(-7)
-4/1 + -14/9= -36/9 + -14/9= -50/9= -5.5
Y=-5.5
Are my answers correct?
The distance from a to b is b-a. So, you should have started out with
8+2/9 (-6 - 8)
Your next line, oddly enough is correct.
Unfortunately at the end, 44/18 ≠ 3 (54/18 = 3)
Y is correct, though you should have just left the answer as -50/9
That is exact, while 5.5 is just an approximation
My new answer for X is 44/9 is that correct?
To verify if your answer is correct, we can use the distance formula. The distance formula is used to find the distance between two points in a coordinate plane.
In this case, we can find the distance of AB, and then find the distance of AP and see if it forms a 2:7 ratio.
The distance formula is given by:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
For AB:
x1 = 8, y1 = -4
x2 = -6, y2 = -11
Using the distance formula, we can find the length of AB:
d_AB = sqrt((-6 - 8)^2 + (-11 - (-4))^2)
= sqrt((-14)^2 + (-7)^2)
= sqrt(196 + 49)
= sqrt(245)
≈ 15.65
Now, let's find the length of AP:
Based on the given ratio, the length of AP is 2/7 of AB.
AP = (2/7) * AB
= (2/7) * 15.65
≈ 4.47
Now, we need to find the coordinates of P.
To find the x-coordinate of point P, we can use the formula:
x-coordinate of P = (2/7) * (x-coordinate of B) + (5/7) * (x-coordinate of A)
= (2/7) * (-6) + (5/7) * 8
= (-12/7) + (40/7)
= 28/7
= 4
To find the y-coordinate of point P, we can use the formula:
y-coordinate of P = (2/7) * (y-coordinate of B) + (5/7) * (y-coordinate of A)
= (2/7) * (-11) + (5/7) * (-4)
= (-22/7) + (-20/7)
= -42/7
= -6
Therefore, the coordinates of point P are (4, -6).
Comparing your answer with the calculated answer, it seems that your answers were incorrect. The correct coordinates of P are (4, -6), not (3, -5.5).
I hope this explanation helps you understand how to use the distance formula and find the coordinates of a point using ratios. Let me know if you have any further questions!