A line segment has endpoints at (5 ,6 ) and (6 , 1). The line segment is dilated by a factor of 2 around (4 , 2). What are the new endpoints and length of the line segment?
1 Answer
Jan 14, 2018
Explanation:
"let "A(5,6) ,B(6,1)" and "D(4,2)
" then "A'" and "B'" are the images of A and B under"
"the dilatation"
rArrvec(DA')=color(red)(2)vec(DA)
rArrula'-uld=2(ula-uld)
rArrula'-uld=2ula-2uld
rArrula'=2ula-uld
color(white)(xxxx)=2((5),(6))-((4),(2))
color(white)(xxxx)=((10),(12))-((4),(2))=((6),(10))
rArrA'(6,10)
"similarly"
vec(DB')=color(red)(2)vec(DB)
rArrulb'-uld=2(ulb-uld)
rArrulb'=2ulb-uld
color(white)(xxxx)=2((6),(1))-((4),(2))=((8),(0))
rArrB'(8,0)
"to calculate length of segment use the "color(blue)"distance formula"
•color(white)(x)d=sqrt((x_2-x_1)^2+(y_2-y_1)^2)
"let "(x_1,y_1)=(6,10)" and "(x_2,y_2)=(8,0)
d=sqrt((8-6)^2+(0-10)^2)=sqrt104~~10.2" 1 dec. place"
