Question

point a is at (6, -6) and point c is at (-6, -2). find the coordinates of point b on $overline{ac}$ such that $ab=\frac{3}{4}ac$. $b = (square,square)$

Explanation:

Step1: Find the difference in x - coordinates

Let \(A(x_1,y_1)=(6, - 6)\) and \(C(x_2,y_2)=(-6,-2)\). The difference in x - coordinates \(\Delta x=x_2 - x_1=-6 - 6=-12\).

Step2: Find the x - coordinate of B

We know that \(AB=\frac{3}{4}AC\). The x - coordinate of \(B\), \(x=x_1+\frac{3}{4}\Delta x\). Substitute \(x_1 = 6\) and \(\Delta x=-12\) into the formula: \(x = 6+\frac{3}{4}\times(-12)=6 - 9=-3\).

Step3: Find the difference in y - coordinates

The difference in y - coordinates \(\Delta y=y_2 - y_1=-2-(-6)=4\).

Step4: Find the y - coordinate of B

The y - coordinate of \(B\), \(y=y_1+\frac{3}{4}\Delta y\). Substitute \(y_1=-6\) and \(\Delta y = 4\) into the formula: \(y=-6+\frac{3}{4}\times4=-6 + 3=-3\).

Answer:

\((-3,-3)\)