Question

The coordinates of the endpoints of EF are E(1,15) and F(15,8). Point G is on EF and divides it such that EG:FG is 5:1. What are the coordinates of G?

a) (3, 12)
b) (5, 11)
c) (7, 10)
d) (9, 9)

Answer 1

Using the section formula to divide the line segment EF in the ratio 5:1, the coordinates of point G calculated are (14, 10). This answer is not listed in the provided options, indicating a potential error in the question's choices.

Step-by-step explanation:

To find the coordinates of point G which divides the line segment EF in the ratio 5:1, we use the section formula (also known as the internal division formula). The coordinates of E are (1,15) and of F are (15,8). Let the ratio be m:n; in this case, m=5 and n=1. The x-coordinate of G is given by: ((m × x2) + (n × x1)) / (m+n) , which boils down to ((5 × 15) + (1 × 1)) / (5+1) = 14.

The y-coordinate of G is given by: ((m × y2) + (n × y1)) / (m+n) , which simplifies to ((5 × 8) + (1 × 15)) / (5+1) = 9.5, rounded to the nearest whole number, we have 10. Therefore, the coordinates of G are (14, 10), which is not listed in the options, suggesting a possible typo in the multiple-choice answers.