Answer:
1. Perpendicular; 2, perpendicular
Step-by-step explanation:
1. Segments JK and LM
(a) Calculate the slopes of the segments
(i) Segment JK
[tex]m_{1} = \dfrac{4 - 9 }{7 - 1} = -\dfrac{5}{6}[/tex]
(ii) Segment LM
[tex]m_{2} = \dfrac{13 - 1 }{8 - (-2)} = \dfrac{12}{8 + 2} = \dfrac{12}{10 } = \dfrac{6}{5}[/tex]
(b) Compare their slopes
[tex]m_{2} =\dfrac{6}{5} = -\dfrac{1}{m_{1}}[/tex]
The two segments are perpendicular.
Their graphs are shown in Figure 1.
2. Equations
(a) Calculate the slopes of the segments
(i) First equation
4x + 5y = 10
5y = 10 - 4x
y = 2 - ⅘x
m₁ = -⅘
(ii) Second equation
5x - 4y = -28
-4y = -28 - 5x
y = 7 + ⁵/₄x
m₂ = ⁵/₄
(b) Compare the slopes
m₂ = ⁵/₄ = -1/m₁
[tex]m_{2} =\dfrac{5}{4} = -\dfrac{1}{m_{1}}[/tex]
The two lines are perpendicular.
The graphs are shown in Figure 2.
