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3 years ago

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Arthur earned 136$ in three weeks. He goes back to school in one more week. He needs at least 189$ to buy the new coat they he w

ants for school. How much must Arthur earn in the next week

1 answer:

saul85 [17]3 years ago

3 0

Answer:

189 minus 136 equals 53 so the answer is 53 dollars

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alisha [4.7K]

Answer:

$d=3\sqrt{2}\ units$

Step-by-step explanation:

<u><em>The complete question is</em></u>

Line L contains points (3, 5) and (7, 9). Points P has coordinates (2, 10). Find the distance from P to L

step 1

Find the equation of the line L contains points (3,5) and (7,9)

<em>Find the slope</em>

The formula to calculate the slope between two points is equal to

$m=\frac{y2-y1}{x2-x1}$

substitute the given values

$m=\frac{9-5}{7-3}$

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<em>Find the equation of the line in point slope form</em>

$y-y1=m(x-x1)$

we have

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substitute

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isolate the variable y

$y=x-3+5$

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step 2

Find the equation of the perpendicular line to the given line L that passes through the point P

Remember that

If two lines are perpendicular, then their slopes are opposite reciprocal

so

The slope of the given line L is $m=1$

The slope of the line perpendicular to the given line L is

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<em>Find the equation of the line in point slope form</em>

$y-y1=m(x-x1)$

we have

$m=-1\\point\ (2,10)$

substitute

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isolate the variable y

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$y=-x+12$ ----> equation B

step 3

Find the intersection point equation A and equation B

$y=x+2$ -----> equation A

$y=-x+12$ ----> equation B

solve the system by graphing

The intersection point is (5.7)

see the attached figure

step 4

we know that

The distance from point P to the the line L is equal to the distance between the point P and point (5,7)

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

we have

(2,10) and (5,7)

substitute

$d=\sqrt{(7-10)^{2}+(5-2)^{2}}$

$d=\sqrt{(-3)^{2}+(3)^{2}}$

$d=\sqrt{18}\ units$

simplify

$d=3\sqrt{2}\ units$

see the attached figure to better understand the problem

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