What are the coordinates of the point drawn in Figure 9.1.1? Draw segments from the point \(P\) to the vertical and horizontal axes to demonstrate the measurements of the coordinates.
On the plot below, graph and label the following points: \(P_1=(0,1)\text{,}\)\(P_2=(1,0)\text{,}\)\(P_3=(2,-3)\text{,}\)\(P_4=(3,-2)\text{,}\)\(P_5=(-3,2)\text{.}\)
Give the coordinates of four points on the horizontal axis. What aspect do all of the points on the horizontal axis have in common? Use this idea to write an equation for the horizontal axis.
Draw a plot of the points \((-1,2)\) and \((7,-4)\text{.}\) On your plot, draw the line segment that measures the distance between the given points and the segments that measure the horizontal and vertical changes. Your plotted segments should make a right triangle.
Find the length of each of line segments in the plot that is your answer to part 9.1.1.e. Explain how the right triangle idea you drew can be generalized to find the distance between two points \((x_1,y_1)\) and \((x_2,y_2)\text{.}\)
