Answer:
(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?
Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.
(b) Write and expression for the slope of line r:
(k-n)/(j-m)
(c) Write and expression for the slope of line s:
(k-n)/(j-m)
(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?
The coordinates of P'' are:
P''=(m,n+ϴ-3)
Step-by-step explanation:
(a) A translation is a rigid transformation. How does this statement support line s being parallel to line r?
Because ALL of the points of line r move the same distance in the same direction, then the inclination of the line s doesn't change with respect line r.
(b) Write and expression for the slope of line r.
Line r goes through the points:
P=(m,n)=(xp,yp)→xp=m, yp=n
Q=(j,k)=(xq,yq)→xq=j, yq=k
Slope of line r is:
mr=(yq-yp)/(xq-xp)
Replacing the coordinates, the expression for the slope of line r is:
mr=(k-n)/(j-m)
(c) Write and expression for the slope of line s.
Line s goes through the points:
P'=(m,n+ϴ)=(xp',yp')→xp'=m, yp'=n+ϴ
Q'=(j,k+ϴ)=(xq',yq')→xq'=j, yq'=k+ϴ
Slope of line s is:
ms=(yq'-yp')/(xq'-xp')
Replacing the coordinates, the expression for the slope of line s is:
ms=[(k+ϴ)-(n+ϴ)]/(j-m)
Eliminating the parentheses in the numerator:
ms=[k+ϴ-n-ϴ]/(j-m)
Simplifyng:
ms=(k-n)/(j-m)
(d) Line q is a vertical is a vertical translation of line s 3 units down. P'' is the image of P'. What are the coordinates of P''?
3 units down, then change only the ordinate y:
P''=(xp',yp'-3)
Replacing xp' and yp':
P''=(m,n+ϴ-3)
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