\displaystyle\text{Find the point on the y-axis that is 6 units

Tobias Ali

Tobias Ali

Answered question

2021-08-15

Find the point on the y-axis that is 6 units from the point {({6},{3})}

Answer & Explanation

Elberte

Elberte

Skilled2021-08-16Added 95 answers

Let{({x}{1},{y}{1})}={({0},{y})}be the point on the y-axis. We also let{({x}{2},{y}{2})}={({6},{3})}.
Use the distance formula to find y where d=6:
{d}={{({x}{2}{x}{1})}2+{({y}{2}{y}{1})}2}
{6}={{({6}{0})}2+{({3}{y})}2}
{6}={36}+{9}+{6}{y}+{y}2
{6}={y}2+{6}{y}+{45}
Square both sides:
{36}={y}2+{6}{y}+{4}
Subtract 36 from both sides:
{0}={y}2+{6}{y}+{9}
Factor:
{0}={({y}+{3})}{({y}+{3})}
By zero product property,
{y}={3}
So, the point that is 6 units from (-6,-3)is:
{({0},{3})}

Do you have a similar question?

Recalculate according to your conditions!

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?