Question

Determine the location of point L
if it divides AB¯¯¯¯¯¯¯¯
into two segments in the ratio 1:3.

(1 point)
Responses

(−12,34)
left parenthesis negative Start Fraction 1 over 2 End Fraction comma Start Fraction 3 over 4 End Fraction right parenthesis

(−23,1)
left parenthesis negative Start Fraction 2 over 3 End Fraction comma 1 right parenthesis

(1,−32)
left parenthesis 1 comma negative Start Fraction 3 over 2 End Fraction right parenthesis

(14,14)
left parenthesis Start Fraction 1 over 4 End Fraction comma Start Fraction 1 over 4 End Fraction right parenthesis

Answer 1

To determine the location of point L that divides the line segment AB in the ratio 1:3, we can use the section formula. The section formula states that if a point L divides the line segment joining two points A(x1, y1) and B(x2, y2) in the ratio m:n, then the coordinates of point L are given by:

\[
L \left( \frac{mx_2 + nx_1}{m+n}, \frac{my_2 + ny_1}{m+n} \right)
\]

Here, the given information states that L divides AB into segments in the ratio 1:3. This means \(m = 1\) and \(n = 3\).

However, to use this formula, we need the coordinates of points A and B. Since the coordinates of A and B are not provided in your question, we can't apply the section formula directly.

Please provide the coordinates of points A and B so that we can find the coordinates of point L. Without information on A and B, we cannot determine the location of point L among the options provided.