#5
Given AC line segment with A(3, 4) and C(-9, -2), if B partitions AC such that the ratio of AB to BC is 1:5, find the coordinates of B.
My answer:
B=(1, 3)
Is this correct?
good again
Yay! I just am trying to see the more and more I do this that I am on the right track.
Thank you
To find the coordinates of point B, we can use the ratio of AB to BC to divide the line segment AC into 6 equal parts (1 unit for AB and 5 units for BC).
Step 1: Find the x-coordinate of point B:
Let's first find the change in x-coordinates between points A and C:
Δx = x_C - x_A = -9 - 3 = -12
To find the change in x-coordinate for each part, we divide Δx by the number of parts (6):
Δx_part = Δx / 6 = -12 / 6 = -2
Starting from the x-coordinate of point A, we add 1 part (Δx_part) to get the x-coordinate of point B:
x_B = x_A + Δx_part = 3 + (-2) = 1
Step 2: Find the y-coordinate of point B:
Let's first find the change in y-coordinates between points A and C:
Δy = y_C - y_A = -2 - 4 = -6
To find the change in y-coordinate for each part, we divide Δy by the number of parts (6):
Δy_part = Δy / 6 = -6 / 6 = -1
Starting from the y-coordinate of point A, we add 1 part (Δy_part) to get the y-coordinate of point B:
y_B = y_A + Δy_part = 4 + (-1) = 3
So, the coordinates of point B are (1, 3).
Your answer is correct! Well done!
To find the coordinates of point B, you can use the concept of section formula.
The section formula states that if a line segment AB is partitioned by a point P in the ratio m:n, then the coordinates of point P can be found using the following formulas:
x-coordinate of point P = (n * x-coordinate of A + m * x-coordinate of B) / (m + n)
y-coordinate of point P = (n * y-coordinate of A + m * y-coordinate of B) / (m + n)
In this case, the ratio of AB to BC is 1:5, which means m = 1 and n = 5.
Let's calculate the coordinates of point B using the section formula:
x-coordinate of point B = (5 * x-coordinate of A + 1 * x-coordinate of C) / (1 + 5)
= (5 * 3 + 1 * (-9)) / 6
= (15 - 9) / 6
= 6 / 6
= 1
y-coordinate of point B = (5 * y-coordinate of A + 1 * y-coordinate of C) / (1 + 5)
= (5 * 4 + 1 * (-2)) / 6
= (20 - 2) / 6
= 18 / 6
= 3
Therefore, the coordinates of point B are B(1, 3).
Based on your answer, B=(1, 3), it seems to be correct. Well done!