Question
the segment XY X(-1,2) , Y(4,11) is to be extended to point Z which is 4 itmes the length of XY. Find the coordinates of Z
Answers
Reiny
let the new point be (x,y)
I will assume you mean XZ = 4XY
by simple ratio:
for the x's
(x+1)/(4+1) = 4/1
x+1 = 20
x = 19
for the y's
(y-2)/(11-2) = 4/1
y-2 = 36
y = 38
Z is (19,38)
check:
XY = √(5^2 + 9^2) = √106
XZ = √(20^2 + 36^2) = √1696 = 4√106
my answer is correct
I will assume you mean XZ = 4XY
by simple ratio:
for the x's
(x+1)/(4+1) = 4/1
x+1 = 20
x = 19
for the y's
(y-2)/(11-2) = 4/1
y-2 = 36
y = 38
Z is (19,38)
check:
XY = √(5^2 + 9^2) = √106
XZ = √(20^2 + 36^2) = √1696 = 4√106
my answer is correct