Mathematics, 27.06.2019 07:30 kenyasutton10

Find the coordinates of the orthocenter of △ a b c with vertices a(-3,3), b(-1,7), and c(3,3). you must show all of your steps.

Find the coordinates of the orthocenter of △ a b c with vertices a(-3,3), b(-1,7), and c(3,3). you m

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Answer from: bloodyflower2003

( -1,-5 )

Step-by-step explanation:

We have the co-ordinates A( -3,3 ), B( -1,7 ) and C( 3,3 ).

We will find the orthocenter using below steps:

1. First, we find the equations of AB and BC.

The general form of a line is y=mx+b where m is the slope and b is the y-intercept.

Using the formula of slope given by $m=\frac{y_{2}-y_{1}}{x_{2}-x_{1} }$ , we will find the slope of AB and BC.

Now, slope of AB is $m=\frac{7-3}{-1+3}$ i.e. $m=\frac{4}{2}$ i.e. m=2 .

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = 2 × (-1) + b i.e. b = 3.

So, the equation of AB is y = 2x + 3.

Also, slope of BC is $m=\frac{3-7}{3+1}$ i.e. $m=\frac{-4}{4}$ i.e. m=-1 .

Putting this 'm' in the general form and using the point B( -1,1 ), we get the y-intercept as,

y = mx + b i.e. 1 = (-1) × (-1) + b i.e. b = 0.

So, the equation of BC is y = -x.

2. We will find the slope of line perpendicular to AB and BC.

When two lines are perpendicular, then the product of their slopes is -1.

So, slope of line perpendicular to AB is $m \times 2 = -1$ i.e. $m=\frac{-1}{2}$

So, slope of line perpendicular to BC is $m \times (-1) = -1$ i.e. m = 1.

3. We will now find the equations of line perpendicular to AB and BC.

Using the slope of line perpendicular to AB i.e. $m=\frac{-1}{2}$ and the point opposite to AB i.e. C( 3,3 ), we get,

y = mx+b i.e. $3=\frac{-1}{2} \times 3 + b$ i.e. $b=\frac{9}{2}$

So, the equation of line perpendicular to AB is $y=\frac{-x}{2} +\frac{9}{2}$

Again, using the slope of line perpendicular to BC i.e. m = 1 and the point opposite to BC i.e. A( -3,3 ), we get,

y = mx + b i.e. 3 = 1 × -3 + b i.e. b = 6.

So, the equation of line perpendicular to BC is y = x+6

4. Finally, we will solve the obtained equations to find the value of ( x,y ).

As, we have y = x+6 and $y=\frac{-x}{2}+\frac{9}{2}$

This gives, $y=\frac{-x}{2}+\frac{9}{2}$ → $x+6=\frac{-x}{2} +\frac{9}{2}$ → 2x+12 = -x+9 → 3x = -3 → x = -1.

So, y = x+6 → y = -1+6 → y=5.

Hence, the orthocenter of the ΔABC is ( -1,5 ).

Answer from: Quest

597

step-by-step explanation:

Answer from: Quest

the correct answer is you spend $55.78 more in a brand store that buy ing in a normal store.

step-by-step explanation:

brand = spend $ 135.85 total

store = spend $80.07 total

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Find the coordinates of the orthocenter of △ a b c with vertices a(-3,3), b(-1,7), and c(3,3). you m...