A line segment has endpoints at (5 ,9 ) and (6 ,7 ). The line segment is dilated by a factor of 2 around (5 ,3 ). What are the new endpoints and length of the line segment?
1 Answer
Jul 27, 2018
Explanation:
"let "A=(5,9),B=(6,7)" and "C=(5,3)" then"
vec(CA')=2vec(CA)" where A' is the image of A"
ula'-ulc=2ula-2ulc
ula'=2ula-ulc
color(white)(ula')=2((5),(9))-((5),(3))
color(white)(ula')=((10),(18))-((5),(3))=((5),(15))
rArrA'=(5,15)
"Similarly "
ulb'=2ulb-ulc
color(white)(ulb')=2((6),(7))-((5),(3))
color(white)(ulb')=((12),(14))-((5),(3))=((7),(11))
rArrB'=(7,11)
"calculate the length using 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)=(7,11)" and "(x_2,y_2)=(5,15)
d=sqrt((5-7)^2+(15-11)^2
color(white)(d)=sqrt(4+16)=sqrt20=2sqrt5
