Question

A (0,0)
B (-8,2)

Determine the coordinates of point C that divides AB into two segments in the ratio 1:4. Write your responses as decimal values (if necessary) to the tenths place.

C is located at (_,_)

Answer 1

To find the coordinates of point C that divides the segment AB in the ratio 1:4, we can use the section formula.

Given points A (0,0) and B (-8,2), the coordinates of point C that divides AB in the ratio \( m:n = 1:4 \) can be calculated using the formula:

\[
C(x, y) = \left( \frac{m x_2 + n x_1}{m+n}, \frac{m y_2 + n y_1}{m+n} \right)
\]

where:
- \( (x_1, y_1) \) are the coordinates of point A,
- \( (x_2, y_2) \) are the coordinates of point B,
- \( m \) and \( n \) are the parts of the ratio.

Substituting the values:
- \( A(0, 0) \): \( x_1 = 0, y_1 = 0 \)
- \( B(-8, 2) \): \( x_2 = -8, y_2 = 2 \)
- \( m = 1, n = 4 \)

Now, calculating the coordinates of point C:

\[
C(x) = \frac{1 \cdot (-8) + 4 \cdot 0}{1 + 4} = \frac{-8 + 0}{5} = \frac{-8}{5} = -1.6
\]

\[
C(y) = \frac{1 \cdot 2 + 4 \cdot 0}{1 + 4} = \frac{2 + 0}{5} = \frac{2}{5} = 0.4
\]

Therefore, the coordinates of point C are:

\[
C(-1.6, 0.4)
\]

Thus, C is located at **(-1.6, 0.4)**.