Question

Coordinate geometry help

Answer 1

Answer: 5a. (15, -3)    5b. 5x - 7y - 26 = 0     5c. (15, 7)

Step-by-step explanation:

5a) D is the Midpoint of A and C.

                 $D_x=\dfrac{A_x+C_x}{2}\qquad \qquad \qquad D_y=\dfrac{A_y+C_y}{2}\\\\\\8=\dfrac{1+p}{2}\qquad \qquad \qquad \qquad \quad 2=\dfrac{7+q}{2}$

                 16 = 1 + p                                 4 = 7 + q

                 15 = p                                   -3 = q

                                       D = (15, -3)

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5b) Find the perpendicular slope and use the Point-Slope formula.

$m=\dfrac{y_A-y_D}{x_A-x_D}\quad =\dfrac{1-8}{7-2}\quad =\dfrac{-7}{5}\quad \rightarrow \quad m_{\perp}=\dfrac{5}{7}$

$y-y_D=m(x-x_D)\\\\y-2=\dfrac{5}{7}(x-8)\\\\\\7(y-2)=5(x-8)\\\\7y-14=5x-40\\\\0=5x-7y-40+14\\\\\bold{5x-7y-26=0}$

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5c) line AE: y = 7

     line DE: 5x - 7y - 26 = 0

Use Substitution method to solve the system for x, given that y = 7:

                  5x - 7(7) - 26 = 0

                   5x - 49 - 26 = 0

                    5x - 75 = 0

                           5x = 75

                            x = 15                          y = 7

                                           E = (15, 7)