Question

what are the x - and y - coordinates of point c, which partitions the directed line segment from a to b into the ratio 3:10? round to the nearest tenth, if necessary x = y =

Explanation:

Step1: Find the coordinates of points A and B

From the graph, $A(-5,8)$ and $B(1,-4)$

Step2: Use the section formula

The section formula for a point \(C(x,y)\) that divides the line segment from \(A(x_1,y_1)\) to \(B(x_2,y_2)\) in the ratio \(m:n\) is \(x=\frac{mx_2+nx_1}{m + n}\) and \(y=\frac{my_2+ny_1}{m + n}\)
Here, \(m = 3\), \(n=10\), \(x_1=-5\), \(y_1 = 8\), \(x_2=1\), \(y_2=-4\)

Step3: Calculate the x - coordinate of point C

$$
LATEXBLOCK0
$$

Step4: Calculate the y - coordinate of point C

$$
LATEXBLOCK1
$$

Answer:

$x = - 2.7$, $y = 5.1$