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Sagot :
Answer:
see explanation
Step-by-step explanation:
(a)
The equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
Calculate m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (P(16, 9) and (x₂, y₂ ) = Q(22, 24)
[tex]m_{PQ}[/tex] = [tex]\frac{24-9}{22-16}[/tex] = [tex]\frac{15}{6}[/tex] = [tex]\frac{5}{2}[/tex]
Given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{\frac{5}{2} }[/tex] = - [tex]\frac{2}{5}[/tex] , then
y = - [tex]\frac{2}{5}[/tex] x + c ← is the partial equation
To find c substitute (5, 1) into the partial equation
1 = - 2 + c ⇒ c = 1 + 2 = 3
y = - [tex]\frac{2}{5}[/tex] x + 3 ← equation of perpendicular line
(b)
Given PN = 2NQ , then N sections PQ in the ratio 2 : 1
Using the Section formula to find coordinates of N
N = ( [tex]\frac{16(1)+22(2)}{1+2}[/tex] , [tex]\frac{9(1)+24(2)}{1+2}[/tex] )
= ( [tex]\frac{16+44}{3}[/tex], [tex]\frac{9+48}{3}[/tex] )
= ( [tex]\frac{60}{3}[/tex], [tex]\frac{57}{3}[/tex] )
= (20, 19 )
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