Final answer:
The coordinates of the point that divides the line segment between K(-5,-4) and L(5,1) in a 5 to 2 ratio would be (15/7, -3/7), which approximately simplifies to (2, -0.42857). None of the given answer choices match this correct answer.
Step-by-step explanation:
The student's question pertains to finding the coordinates that divide the line segment between two points K(-5,-4) and L(5,1) into a 5 to 2 ratio. To solve this problem, we employ the concept of the section formula which is used to find a point that divides a line segment into a given ratio.
To find the coordinates of the point (x,y), we use the formula:
x = (mx2 + nx1) / (m+n)
y = (my2 + ny1) / (m+n)
Where (x1,y1) and (x2,y2) are coordinates of points K and L respectively, and m:n is the given ratio.
For the given question:
x = ((5*5) + (2*-5)) / (5+2) = (25-10) / 7 = 15/7
y = ((5*1) + (2*-4)) / (5+2) = (5-8) / 7 = -3/7
So, the coordinates of the point are (15/7, -3/7), which simplifies to approximately (2, -0.42857).
Therefore, none of the options given match the correct answer.