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find the distance from point A(15,-21) to the line 5x + 2y = 4 . round your answer to the nearest tenth

User Peter Howe
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1 Answer

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We will find the distance from point A to the line as follows:

*First: We solve for 0 on the equation of the line, that is:


5x+2y=4\Rightarrow5x+2y-4=0

Now, we can see that the equation of the line has the form:


Ax+Bx+C=0

So, we use the following expression to determine the distance from the point to the line:


d=\fracAx_1+By_1+C{\sqrt[]{A^2+B^2}}

Now, we replace the values and solve for d:


d=\frac(5)(15)+(4)(-21)+(-4){\sqrt[]{5^2+2^2}}\Rightarrow d=\frac-13{\sqrt[]{29}}
\Rightarrow d=\frac{13}{\sqrt[]{29}}\Rightarrow d\approx2.4

So, the distance from point (15, -21) to the line 5x + 2y = 4 is approximately 2.4 units.

User Michel Floyd
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