Question

select the correct answer from each drop - down menu. in the diagram, \\( \overline { a b } \\) is divided into equal parts. the coordinates of point \\( a \\) are \\( ( - 3,9 ) \\), and the coordinates of point \\( b \\) are \\( ( 9,5 ) \\). the coordinates of point \\( c \\) are \\( ( - 1.5,8.5 ) \\). the coordinates of point \\( e \\) are \\( ( 1.5,7.5 ) \\). the coordinates of point \\( h \\) are

Explanation:

Step1: Calculate the change in \(x\) and \(y\) coordinates

The formula for the change in \(x\) - coordinate \(\Delta x=x_B - x_A\), and for \(y\) - coordinate \(\Delta y=y_B - y_A\).
Given \(A(-3,9)\) and \(B(9,5)\), \(\Delta x=9-(-3)=12\), \(\Delta y = 5 - 9=-4\).
Since \(\overline{AB}\) is divided into 8 equal parts.
The increment for \(x\) - coordinate per part is \(\frac{\Delta x}{8}=\frac{12}{8}=1.5\), and for \(y\) - coordinate per part is \(\frac{\Delta y}{8}=\frac{-4}{8}=-0.5\).

Step2: Find the coordinates of point \(H\)

Point \(H\) is 6 parts away from point \(A\) (counting from \(A\)).
For \(x\) - coordinate of \(H\): \(x_A+6\times1.5=-3 + 6\times1.5=-3+9 = 6\)
For \(y\) - coordinate of \(H\): \(y_A+6\times(-0.5)=9+6\times(-0.5)=9 - 3=6\)

Answer:

\((6,6)\)