Final answer:
The point that divides the directed line segment BC two-fifths from B to C has an x-coordinate of 5, which is calculated using the section formula.
Step-by-step explanation:
To find the point that divides the directed line segment BC into a ratio of two-fifths from B to C, we will use the formula for a point dividing a line in a given ratio, which is often referred to as the section formula.
If B has coordinates (x1, y1) and C has coordinates (x2, y2), and we are dividing the line in the ratio m:n, the coordinates of the dividing point P (xp, yp) can be found by:
- xp = (mx2 + nx1) / (m + n)
- yp = (my2 + ny1) / (m + n)
In this case, m = 2 and n = 3 because we want to divide segment BC two-fifths from B, meaning the ratio is 2:3. The coordinates of B are (3, 5) and C is (8, -5).
Applying this to the x-coordinate formula:
xp = (2×8 + 3×3) / (2 + 3) = (16 + 9) / 5 = 25 / 5 = 5
Therefore, the x-coordinate of the point that divides BC two-fifths from B to C is 5.