Question

what are the coordinates of the point that is $\frac{3}{5}$ of the way from $a(-9,3)$ to $b(21,-2)$?
a. $(9,1)$
b. $(3,1)$
c. $(-7,2)$
d. $(9,0)$

Explanation:

Step1: Calculate x - coordinate

Let \(x_1=-9\), \(x_2 = 21\). The formula for the x - coordinate of the point that divides the line segment from \((x_1,y_1)\) to \((x_2,y_2)\) in the ratio \(m:n\) is \(x=x_1+\frac{m}{m + n}(x_2 - x_1)\). Here \(m = 3\), \(n=2\) (since \(\frac{m}{m + n}=\frac{3}{5}\)), so \(x=-9+\frac{3}{5}(21+9)=-9+\frac{3}{5}\times30=-9 + 18=9\).

Step2: Calculate y - coordinate

Let \(y_1 = 3\), \(y_2=-2\). Using the formula \(y=y_1+\frac{m}{m + n}(y_2 - y_1)\), we have \(y = 3+\frac{3}{5}(-2 - 3)=3+\frac{3}{5}\times(-5)=3-3 = 0\).

Answer:

D. \((9,0)\)