Question 1185691
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The solution method shown by the other tutor is fine.<br>
Here is an alternative method.  If you are solving this kind of problem (finding the shortest distance from a point to a line) frequently, this method will be faster.<br>
(1) Find the equation of line AC in the form Ax+By+C=0.<br>
From A to C the change in x is +6 and the change in y is +3, so the slope is 3/6 = 1/2.  So the equation is of the form y=(1/2)x+b.
Plug in either of the given (x,y) values to determine b.
4=(1/2)(-2)+b
4=-1+b
b=5<br>
The equation of the line in slope-intercept form is y=(1/2)x+5.<br>
Put the equation in the required form.<br>
y=(1/2)x+5
2y=x+10
x-2y+10=0<br>
(2) Use the formula for the (shortest) distance from a point (p,q) to the line with equation Ax+By+C=0:<br>
{{{abs((Ap+Bq+C)/sqrt(A^2+B^2))}}}
{{{abs((1(2)+(-2)(-2)+10)/sqrt(1^2+2^2)) = abs(16/sqrt(5)) = 16/sqrt(5)}}}<br>
ANSWER: 7.1554 to 4 decimal places<br>