Line segment AB is divided by point C in the ratio 1:2. Point A is at (-6, 6) and point C is at (2, 4). What are the coordinates of point B?
B = A + 3AC = (-6,6) + 3(8,-2) = (-6,6)+(24,-6) = (18,0)
yass thank you queenb
wait actually where did you get 3(8,2) from?
To find the coordinates of point B, we can use the concept of dividing a line segment in a given ratio.
First, let's calculate the distance between points A and C:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Distance = √((2 - (-6))^2 + (4 - 6)^2)
= √((2 + 6)^2 + (-2)^2)
= √(8^2 + 4)
= √(64 + 4)
= √68
≈ 8.246
Since point C divides the line segment in the ratio 1:2, we can determine the coordinates of point B using the following formula:
B = (x2, y2) = (x1 + (2/3) * (x2 - x1), y1 + (2/3) * (y2 - y1))
Plugging in the known values:
(2, 4) = (-6 + (2/3) * (x2 - (-6)), 6 + (2/3) * (y2 - 6))
Simplifying the equation:
2 = (-6 + (2/3) * (x2 + 6))
4 = (6 + (2/3) * (y2 - 6))
Now we can solve for x2 and y2:
2 = (-6 + (2/3) * (x2 + 6))
2 = (2/3) * (x2 + 6)
3 = x2 + 6
x2 = -3
4 = (6 + (2/3) * (y2 - 6))
4 = (2/3) * (y2 - 6)
6 = y2 - 6
y2 = 12
Therefore, the coordinates of point B are (-3, 12).