Question

find the coordinates of the point $\frac{7}{10}$ of the way from a to b.
a(-3,-7)
b(11,6)
the coordinates of the point $\frac{7}{10}$ of the way from a to b are
(type an ordered pair.)

Explanation:

Step1: Recall the section - formula

If a point $P(x,y)$ divides the line - segment joining $A(x_1,y_1)$ and $B(x_2,y_2)$ in the ratio $m:n$, then $x=\frac{mx_2+nx_1}{m + n}$ and $y=\frac{my_2+ny_1}{m + n}$. Here, $m = 7$, $n=10 - 7=3$, $x_1=-3$, $y_1=-7$, $x_2 = 11$, and $y_2 = 6$.

Step2: Calculate the x - coordinate

$x=\frac{7\times11+3\times(-3)}{7 + 3}=\frac{77-9}{10}=\frac{68}{10}=6.8$.

Step3: Calculate the y - coordinate

$y=\frac{7\times6+3\times(-7)}{7 + 3}=\frac{42-21}{10}=\frac{21}{10}=2.1$.

Answer:

$(6.8,2.1)$