+0  
 
0
163
1
avatar

Please help me!

 

i) Find the equation of BC

ii) Find the coordinates of D

iii)Find the angle that CD makes with the positive x axis.

 

Thank you!

Guest Mar 2, 2017
edited by Guest  Mar 2, 2017
edited by Guest  Mar 2, 2017
 #1
avatar+19653 
+5

Please help me!

 

i) Find the equation of BC

slope BA: \(\begin{array}{|rcll|} \hline m = \frac{y_A-y_B}{x_A-x_B} \\ \hline \end{array}\)

slope BC: \(\begin{array}{|rcll|} \hline m_{\perp} = -\frac{1}{m} &=& -\frac{x_A-x_B}{y_A-y_B} \\ \hline \end{array}\)

 

Equation of BC:

\(\begin{array}{|rcll|} \hline m_{\perp} = \frac{y -y_B}{x -x_B} &=& -\frac{x_A-x_B}{y_A-y_B} \\ & \dots & \\ y &=& -\left(\frac{x_A-x_B}{y_A-y_B}\right)\cdot (x-x_B) + y_B \\ && x_B = -2 \quad y_B = 8 \qquad x_A = 2 \quad y_A = 14 \\ &=& -\left[\frac{2-(-2)}{14-8}\right]\cdot [x-(-2)] + 8 \\ &=& -\frac{4}{6}\cdot (x+2) + 8 \\ &=& -\frac{2}{3}\cdot (x+2) + 8 \\ \mathbf{y} & \mathbf{=} & \mathbf{-\frac{2}{3}\cdot x + \frac{20}{3}} \\ \hline \end{array}\)

 

ii) Find the coordinates of D

 

coordinates of C ( \(y_C=0\) )

\(\begin{array}{|rcll|} \hline 0 & = & -\frac{2}{3}\cdot x_C + \frac{20}{3} \\ \frac{2}{3}\cdot x_C &=& \frac{20}{3} \\ x_C &=& \frac{20}{3}\cdot \frac{3}{2} \\ \mathbf{x_C} & \mathbf{=} & \mathbf{10} \\ \hline \end{array}\)

C is (10,0)

 

coordinates of D:

\(\begin{array}{|rcll|} \hline x_D &=& x_C + (x_A-x_B) \\ x_D &=& 10 + [2-(-2)] \\ x_D &=& 10 + 4 \\ \mathbf{x_D} & \mathbf{=} & \mathbf{14} \\\\ y_D &=& y_C + (y_A-y_B) \\ y_D &=& 0 + (14-8) \\ \mathbf{y_D} & \mathbf{=} & \mathbf{6} \\ \hline \end{array} \)

D is (14,6)

 

iii) Find the angle that CD makes with the positive x axis.

\(\begin{array}{|rcll|} \hline \varphi &=& \arctan(m) \quad & | \quad m = \frac{y_A-y_B}{x_A-x_B} = \frac{14-8}{2-(-2)}=\frac{6}{4}=\frac32 \\ \varphi &=& \arctan(\frac32) \\ \varphi &=& \arctan(1.5) \\ \mathbf{\varphi} & \mathbf{=} & \mathbf{56.3099324740^{\circ} } \\ \hline \end{array} \)

 

 

laugh

heureka  Mar 2, 2017
edited by heureka  Mar 2, 2017
edited by heureka  Mar 2, 2017

7 Online Users

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.