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Illusion [34]
3 years ago
7

Write the equation of the line that is perpendicular to the line y = 2x + 2 and passes through the point (6, 3).

Mathematics
1 answer:
weeeeeb [17]3 years ago
5 0

Answer:

\[y = (-1/2) * x + 6\]

Step-by-step explanation:

Equation of the given line: y=2x+2

Hence the slope of the line is given by 2

Any line which is perpendicular to the given line will have a slope m such that m*2 = -1

Or, \[m = \frac{-1}{2}\]

Only options 2 and 3 satisfy this condition.

The line is also supposed to pass through the point (6,3).

Substituting these values in the option 2:

\[3 = (-1/2) * 6 + 3\]

Or, \[ 3 =0 \] which is false . Hence option 2 is not valid.

Now substituting (6,3) in option 3:

\[3 = (-1/2) * 6 + 6\]

Or, \[ 3 =3 \] which is true . Hence option 3 is the required equation of the line.

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We have the points G(1, 4) and H(3, 0), to get the distance between them we use the distance formula, we will get:

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