Question

5. Draw 2 line segment of different lengths that both have M as a midpoint.

Answer 1

Step 1: Write out the coordinate of the midpoint

$M(-2,-3)$

Step 2: Find the coordinates of the two line segments by testing for values that will yeild the midpoint coordinates

$\begin{gathered} \text{ Since the midpoint M is at (-2,-3), then} \\ M(-2,-3)\Rightarrow(x_m,y_m) \\ x_m=\frac{x_1+x_2}{2}=-2 \\ y_m=\frac{y_1+y_2}{2}=-3 \end{gathered}$$\begin{gathered} \text{Thus,} \\ x_1+x_2=-2(2)=-4 \\ y_1+y_2=-3(2)=-6 \end{gathered}$

From the above, we can deduce to four values that will give -4 for the x-values and -6 for the y-values.

$\begin{gathered} \text{For the first line segment},\text{ say line AB} \\ x_1+x_2=-6+2=-4,x_1=-6,x_2=2 \\ y_1+y_2=-9+3=-6,y_1=-9,y_2=3 \\ \text{Therefore, line AB coordinate is } \\ A(-6,-9),B(2,3) \end{gathered}$$\begin{gathered} \text{For the first line segment},\text{ say line CD} \\ x_1+x_2=-10+6=-4,x_1=-10,x_2=6 \\ y_1+y_2=-14+8=-6,y_1=-14,y_2=8 \\ \text{Therefore, line AB coordinate is } \\ C(-10,-14),D(6,8) \end{gathered}$

Step 3: Draw the two lines segment on a cartesian plane showing M as the common midpoint.