Question

the point b lies on the segment (overline{ac}). find the coordinates of b so that (ab) is (\frac{1}{4}) of (ac). a (-28, 22) b (?, ?) c (4, -2) try again

Explanation:

Step1: Find the vector from A to C

The coordinates of \( A(-28, 22) \) and \( C(4, -2) \). The vector \( \overrightarrow{AC} \) is \( (4 - (-28), -2 - 22)=(32, -24) \).

Step2: Find the vector \( \overrightarrow{AB} \)

Since \( AB=\frac{1}{4}AC \), the vector \( \overrightarrow{AB}=\frac{1}{4}\overrightarrow{AC}=\frac{1}{4}(32, -24)=(8, -6) \).

Step3: Find the coordinates of B

The coordinates of \( B \) are \( A+\overrightarrow{AB}=(-28 + 8, 22+(-6))=(-20, 16) \).

Answer:

\((-20, 16)\)