Question

point v lies on tu such that tv:uv is 3:2. graph v.

Explanation:

Step1: Find coordinates of T and U

From the graph, \( T(-8, 7) \) and \( U(-3, -8) \).

Step2: Use section formula

The section formula for a point \( V(x, y) \) dividing a line segment joining \( (x_1, y_1) \) and \( (x_2, y_2) \) in the ratio \( m:n \) is \( x=\frac{mx_2 + nx_1}{m + n} \), \( y=\frac{my_2 + ny_1}{m + n} \). Here, \( m = 3 \), \( n = 2 \), \( (x_1, y_1)=(-8, 7) \), \( (x_2, y_2)=(-3, -8) \).

Step3: Calculate x - coordinate of V

\( x=\frac{3\times(-3)+2\times(-8)}{3 + 2}=\frac{-9-16}{5}=\frac{-25}{5}=-5 \)

Step4: Calculate y - coordinate of V

\( y=\frac{3\times(-8)+2\times7}{3 + 2}=\frac{-24 + 14}{5}=\frac{-10}{5}=-2 \)

Answer:

The coordinates of point \( V \) are \( (-5, -2) \), so we graph the point at \( (-5, -2) \) on the coordinate plane.