Line c passes through points (7, 10) and (5, 19). Line d is perpendicular to c. What is the slope of line d?

Mathematics

1 answer:

muminat3 years ago

3 0

Answer:

2/9

Step-by-step explanation:

slope of line C: (19 - 10) / (5 - 7) = - 9/2

line d perpendicular to Line C, slope of d: 2/9

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If we plot the points and connect them, we get this triangle:

Let point
A=(xA,yA)
B=(xB,yB)
C=(xC,yC)

-------------------------------
Let's find the equation of the segment AB

Start with the general formula

Plug in the given points

Simplify and combine like terms

So the equation of the line through AB is

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Let's find the equation of the segment BC

Start with the general formula

Plug in the given points

Simplify and combine like terms

So the equation of the line through BC is

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Let's find the equation of the segment CA

Start with the general formula

Plug in the given points

Simplify and combine like terms

So the equation of the line through CA is

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So to find the equation of the line that is perpendicular to that goes through the point C(2,-5), simply negate and invert the slope to get

Now plug the slope and the point (2,-5) into

Solve for y and simplify

So the altitude for vertex C is

Now to find the equation of the line that is perpendicular to that goes through the point A(4,5), simply negate and invert the slope to get

Now plug the slope and the point (2,-5) into

Solve for y and simplify

So the altitude for vertex A is

Now to find the equation of the line that is perpendicular to that goes through the point B(-4,1), simply negate and invert the slope to get

Now plug the slope and the point (-4,1) into

Solve for y and simplify

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------------------------------------------------------------
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Plug in into the first equation

Add 2x to both sides and subtract 2 from both sides

Divide both sides by 3 to isolate x

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