Discover answers to your questions with Westonci.ca, the leading Q&A platform that connects you with knowledgeable experts. Connect with a community of experts ready to help you find solutions to your questions quickly and accurately. Explore comprehensive solutions to your questions from knowledgeable professionals across various fields on our platform.
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 )
Thank you for your visit. We're committed to providing you with the best information available. Return anytime for more. Thank you for choosing our platform. We're dedicated to providing the best answers for all your questions. Visit us again. Thank you for visiting Westonci.ca, your go-to source for reliable answers. Come back soon for more expert insights.
