A line segment AE with coordinates A(6,-6) and E(14,2) is divided into four equal segments by points B,C and D calculate the coordinates of C, B and D
Please help me I don't know it our teacher never explained how to do it please....
Please have patience and wait for a geometry teacher to come online.
the x-coordinate changes from 6 to 14, a difference of 8.
Divide that by 4, and you can see that the x-coordinates of B,C,D are 8,10,12
Do the same with the change in y.
Please do a tutorial explaining this
To calculate the coordinates of points B, C, and D, we can divide the line segment AE into four equal segments.
Step 1: Calculate the differences in x-coordinates and y-coordinates between points A and E.
- The difference in x-coordinates is: Δx = 14 - 6 = 8.
- The difference in y-coordinates is: Δy = 2 - (-6) = 8.
Step 2: Divide the differences in x and y by 4 to get the increments for each segment.
- The increment in x-coordinate is: Δx_increment = Δx / 4 = 8 / 4 = 2.
- The increment in y-coordinate is: Δy_increment = Δy / 4 = 8 / 4 = 2.
Step 3: Calculate the coordinates of point B:
- The x-coordinate of point B = x-coordinate of A + Δx_increment = 6 + 2 = 8.
- The y-coordinate of point B = y-coordinate of A + Δy_increment = -6 + 2 = -4.
Therefore, the coordinates of point B are B(8, -4).
Step 4: Calculate the coordinates of point C:
- The x-coordinate of point C = x-coordinate of A + (2 * Δx_increment) = 6 + (2 * 2) = 10.
- The y-coordinate of point C = y-coordinate of A + (2 * Δy_increment) = -6 + (2 * 2) = -2.
Therefore, the coordinates of point C are C(10, -2).
Step 5: Calculate the coordinates of point D:
- The x-coordinate of point D = x-coordinate of A + (3 * Δx_increment) = 6 + (3 * 2) = 12.
- The y-coordinate of point D = y-coordinate of A + (3 * Δy_increment) = -6 + (3 * 2) = 0.
Therefore, the coordinates of point D are D(12, 0).
To summarize:
Point B = B(8, -4)
Point C = C(10, -2)
Point D = D(12, 0)