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
the coordinates of point h are
\\( ( 1.5,6.5 ) \\)
\\( ( 1.5,7.5 ) \\)
\\( ( 2.5,6.5 ) \\)
\\( ( 2.5,7.5 ) \\)

Explanation:

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

The formula for the change in \(x\) is \(\Delta x=x_B - x_A\), and for \(y\) is \(\Delta y=y_B - y_A\).
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 (counting the intervals between \(A\) and \(B\)), the increment for \(x\) is \(\frac{\Delta x}{8}=\frac{12}{8} = 1.5\), and for \(y\) is \(\frac{\Delta y}{8}=\frac{-4}{8}=-0.5\).

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

Point \(E\) is 3 intervals away from \(A\).
For \(x\)-coordinate: \(x_E=x_A+3\times1.5=-3 + 4.5 = 1.5\).
For \(y\)-coordinate: \(y_E=y_A+3\times(-0.5)=9-1.5 = 7.5\).

Answer:

\((1.5,7.5)\)