Question

question 16
1 pts
what are the coordinates of the point 1/4 of the way from a(-6, -3) to b(10, 9) on the line segment ab?
this question will be scored by santiago on your paper.

Explanation:

Step1: Find the difference in x - coordinates

The difference in x - coordinates $\Delta x=x_B - x_A$, where $x_A=-6$ and $x_B = 10$. So, $\Delta x=10-(-6)=16$.

Step2: Find the difference in y - coordinates

The difference in y - coordinates $\Delta y=y_B - y_A$, where $y_A=-3$ and $y_B = 9$. So, $\Delta y=9-(-3)=12$.

Step3: Calculate the x - coordinate of the point

The x - coordinate of the point that is $\frac{1}{4}$ of the way from A to B is $x=x_A+\frac{1}{4}\Delta x$. Substitute $x_A=-6$ and $\Delta x = 16$ into the formula: $x=-6+\frac{1}{4}\times16=-6 + 4=-2$.

Step4: Calculate the y - coordinate of the point

The y - coordinate of the point that is $\frac{1}{4}$ of the way from A to B is $y=y_A+\frac{1}{4}\Delta y$. Substitute $y_A=-3$ and $\Delta y = 12$ into the formula: $y=-3+\frac{1}{4}\times12=-3 + 3=0$.

Answer:

$(-2,0)$