Final answer:
The coordinates of point C that divides the line segment AB 2/5 of the way from A(-5,6) to B(5,1) are approximately (-2,4), which is closest to option (c).
Step-by-step explanation:
The question asks to find the coordinates of point C that divides the line segment AB in a certain ratio. Given the coordinates A(-5, 6) and B(5, 1), we need to divide the line segment so that point C divides it in the ratio of 2 to 5. To do this, we can use the formula for a point that divides a line segment in a given ratio (the section formula). The coordinates of point C can be found using the following equations:
- x-coordinate of C = [(m*n1)+(n*n2)] / (m+n), where m and n are the parts of the ratio, here 2 and 5 respectively, and n1 and n2 are the x-coordinates of A and B.
- y-coordinate of C = [(m*m1)+(n*m2)] / (m+n), where m1 and m2 are the y-coordinates of A and B.
Using the above formula:
- x-coordinate of C = [(2*5) + (5*(-5))] / (2+5) = (10 - 25) / 7 = -15/7 = -2.14 which is approximately equal to -2.
- y-coordinate of C = [(2*1) + (5*6)] / (2+5) = (2 + 30) / 7 = 32/7 = 4.57 which is approximately equal to 4.
So, the coordinates of C would be approximately (-2, 4).
The closest option that matches our result is (c) (-2,4).