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Find the distance from the point Q(6,1) to the line y=-2x 8

User Wirher
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1 Answer

5 votes

To find the distance from a point to a line we can use the formula for the distance between a point and a line. The formula is:

Distance = |Ax + By + C| / sqrt(A^2 + B^2)

Where (x y) is the point and A B and C are the coefficients of the line equation in the form Ax + By + C = 0.

Given the line equation y = -2x + 8 we can rewrite it in the form Ax + By + C = 0 by adding 2x to both sides:

2x + y - 8 = 0

Now we can compare the coefficients:

A = 2

B = 1

C = -8

The point Q(6 1) has coordinates (x y) = (6 1).

Plugging these values into the distance formula we get:

Distance = |(2 * 6) + (1 * 1) - 8| / sqrt(2^2 + 1^2)

= |12 + 1 - 8| / sqrt(4 + 1)

= |5| / sqrt(5)

= 5 / sqrt(5)

= sqrt(5)

Therefore the distance from the point Q(6 1) to the line y = -2x + 8 is sqrt(5) (approximately 2.236).

User Postelrich
by
8.0k points

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