Respuesta :
Answer: [tex]k=18\dfrac{8}{11}[/tex].
Step-by-step explanation:
If a line passing through two points, then
[tex]Slope=\dfrac{y_2-y_1}{x_2-x_1}[/tex]
Endpoints of segment MN have coordinates (0, 0) and (5, 1).
Slope of MN [tex]=\dfrac{1-0}{5-0}=\dfrac{1}{5}[/tex]
The endpoints of segment AB have coordinates [tex]\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)[/tex] and [tex]\left(-2\dfrac{1}{4} , k\right)[/tex].
[tex]A=\left(1\dfrac{1}{22} , 2\dfrac{1}{4}\right)=\left(\dfrac{23}{22} ,\dfrac{9}{4}\right)[/tex]
[tex]B=\left(-2\dfrac{1}{4} , k\right)=\left(-\dfrac{9}{4} , k\right)[/tex].
Slope of AB [tex]=\dfrac{k-\frac{9}{4}}{-\frac{9}{4}-\dfrac{23}{22}}[/tex]
[tex]=\dfrac{\frac{4k-9}{4}}{\frac{-99-46}{44}}[/tex]
[tex]=\dfrac{4k-9}{4}\times \dfrac{44}{-145}[/tex]
[tex]=4k-9\times \dfrac{11}{-145}[/tex]
[tex]=\dfrac{44k-99}{-145}[/tex]
Product of slopes of two perpendicular segments is -1.
Slope of MN × Slope of AB = -1
[tex]\dfrac{1}{5}\times \dfrac{44k-99}{-145}=-1[/tex]
[tex]\dfrac{44k-99}{-725}=-1[/tex]
[tex]44k-99=725[/tex]
[tex]44k=725+99[/tex]
[tex]k=\dfrac{824}{44}[/tex]
[tex]k=\dfrac{206}{11}[/tex]
[tex]k=18\dfrac{8}{11}[/tex]
Therefore, the value of k is [tex]k=18\dfrac{8}{11}[/tex].
Answer:
k=21
Step-by-step explanation:
Find the slope of MN which is 1/5, (use the slope formula.)
Use the slope formula for AB using k as y_2
Substitute and you get k=21
21-2.25/-2.25-1.5=-5
The lines are perpendicular because the slopes are the negative reciprocal of one another.