Question

jennas locker is located in the hallway between her math and science classes, as mapped on the cartesian plane below. the distance between her locker and her math class is twice the distance from her locker to her science class. determine the coordinates of jennas locker. (-15,5) (18,32)

Explanation:

Step1: Use section - formula

Let the coordinates of the locker be $(x,y)$. Let the point of Math class be $A(-15,5)$ and the point of Science class be $B(18,32)$. Given that the distance between the locker and Math class is twice the distance from the locker to Science class, so the locker divides the line - segment joining $A$ and $B$ in the ratio $2:1$. The section formula for a point $(x,y)$ that divides the line - segment joining $(x_1,y_1)$ and $(x_2,y_2)$ in the ratio $m:n$ is $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 2$, $n = 1$, $x_1=-15$, $y_1 = 5$, $x_2=18$, $y_2=32$.

Step2: Calculate the x - coordinate

$x=\frac{2\times18+1\times(-15)}{2 + 1}=\frac{36-15}{3}=\frac{21}{3}=7$.

Step3: Calculate the y - coordinate

$y=\frac{2\times32+1\times5}{2 + 1}=\frac{64 + 5}{3}=\frac{69}{3}=23$.

Answer:

$(7,23)$