SOLUTION: find the point on the y-axis that is equidistant from (6,1) (-2,-3)
Algebra.Com
Question 168890: find the point on the y-axis that is equidistant from (6,1) (-2,-3)
Found 2 solutions by Alan3354, stanbon:
Answer by Alan3354(69443) (Show Source): You can put this solution on YOUR website!
find the point on the y-axis that is equidistant from (6,1) (-2,-3)
----------------------
Interesting problem.
The point will be (0,y). x is zero since it's on the y-axis
Use Pythagoras:
d1^2 = (6-0)^2 + (1-y)^2
d2^2 = (-2-0)^2 + (-3 -y)^2
The two expressions are equal, so
36 + (1-y)^2 = 4 + (-3-y)^2
36 + 1 -2y +y^2 = 4 + 9 + 6y + y^2
24 -2y = 6y
24 = 8y
y = 3
The point is (0,3)
Check:
(6-0)^2 + (1-3)^2 =? (-2-0)^2 + (-3-3)^2
36 + 4 =? 4 + 36
40 = 40, so it's equidistant.
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
find the point on the y-axis that is equidistant from (6,1) (-2,-3)
-------------------------------
The point must have the form (0,y)
----------
Equation:
distance^2 = distance^2
(6-0^2 + (y-6)^2 = (0--2)^2 + (y--30^2
36 + y^2 -12y + 12 = 4 + y^2 +6y + 9
48 + y^2 - 12y = 13 + y^2 + 6y
18y = 35
y = 35/18
-----------------
Ans: (0, 35/18)
==============================
Cheers,
Stan H.
RELATED QUESTIONS
Find the point on the y-axis that is equidistant from (5,1) and... (answered by stanbon)
Find the point on the y-axis that is equidistant from (5,1) and... (answered by lwsshak3)
Find the point on the y-axis that is equidistant from (5,1) and... (answered by josgarithmetic)
Find the point on the y axis that is equidistant from (5,1) and... (answered by solver91311,josgarithmetic)
Find the point y-axis that is equidistant from (5,1) and (-3,... (answered by math_tutor2020,josgarithmetic)
Find the point (o,b) on the y-axis on the y-axis that is equidistant from the points... (answered by robertb)
Find the point (0, b) on the y-axis that is equidistant
from the points (5,5) and... (answered by robertb)
find the point on the y axis that is equidistant from the points (-2,0) and... (answered by Alan3354)
find a point on the x axis that is equidistant from (-1,-1) and... (answered by stanbon)