[IMG]file:///C:/DOCUME%7E1/SHAKEE%7E1/LOCALS%7E1/Temp/moz-screenshot.jpg[/IMG]
Can anybody help me with this question please?
First let's find the point M
The formula for the midpoint is given by:
$\displaystyle \left( \frac {x_1 + x_2}{2}, \frac {y_1 + y_2}{2} \right)$
Using $\displaystyle (x_1,y_1) = A(2,9)$ and $\displaystyle (x_2, y_2) = B(8,7)$, the point M is:
$\displaystyle M = \left( \frac {2 + 8}{2}, \frac {9 + 7}{2} \right) = (5,8)$
Now we can find the slope of the lines connecting M and C, and the slope of the line connecting A and B, if there slopes are the negative inverses of each other (that is, the product of their slopes is -1), then MC is perpendicular to AB.
Let $\displaystyle m_1$ be the slope of the line connecting AB
Let $\displaystyle m_2$ be the slope of the line connecting MC
Now, using $\displaystyle (x_1,y_1) = (2,9) \mbox { and } (x_2,y_2) = (8,7)$
$\displaystyle \Rightarrow m_1 = \frac {y_2 - y_1}{x_2 - x_1} = \frac {7-9}{8-2} = - \frac {1}{3}$
Now, using $\displaystyle (x_1,y_1) = (5,8) \mbox { and } (x_2 , y_2) = (8,18)$
$\displaystyle \Rightarrow m_2 = \frac {18 - 8}{8 - 5} = \frac {10}{3}$
Thus, MC and AB are not perpendicular