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MatroZZZ [7]
3 years ago
15

What the answer to this math problem

Mathematics
1 answer:
olga_2 [115]3 years ago
7 0
The answer is 4.4. C.
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Triangle ABC has vertices A(-5, -2), B(7, -5), and C(3, 1). Find the coordinates of the intersection of the three altitudes
fiasKO [112]

Answer:

The coordinates of the intersection of the three altitudes = (-3.5, -1)

Step-by-step explanation:

The altitude of a triangle is a line which passes through a vertex of the triangle and is perpendicular to the opposite side.

There are therefore three altitudes possible in a triangle, one from each vertex. All three altitudes always intersect at the same point called the orthocenter of the triangle.

Let the triangle ABC have altitudes AD, BE and CF as shown in the attached image to this solution. Let the orthocentre be O.

The point O is the point where all the coordinates AD, BE and CF meet.

Hence, to obtain the coordinates of O, we just need to equate the equations of two of the lines that serve as the altitude.

Before that, we need to c9mpute the equations of the two altitudes that we will use.

Noting that the altitudes are perpendicular to the sides of the triangle, we can compute the slopes of the altitudes from caldilating the slopes of the sides.

Slope of AB

= (y₂-y₁)/(x₂−x₁)

= (-5 - (-2))/(7 - (-5))

= (-3/12)

= (-1/4)

Slope of its altitude, CF

= -1 ÷ (Slope of AB)

= -1 × (-1/4)

= 4

The equation of CF is given using point C as,

y – y₁ = m(x – x₁)

y - 1 = 4 (x – 3)

y - 1 = 4x - 12

y = 4x + 13

Slope of BC

= (y₂-y₁)/(x₂−x₁)

= (1 - (-5))/(3 - 7)

= (6/-4)

= (-3/2)

Slope of AD

= −1 ÷ (Slope of BC)

= -1 ÷ (-3/2)

= (2/3)

The equation of AD using point A given as,

y – y₁ = m(x – x₁)

y – (-2)) = (2/3) (x – (-5))

y + 2 = (2x/3) + (10/3)

y = (2x/3) + (4/3)

Now equation the equations of the altitudes CF and AD

y = 4x + 13

y = (2x/3) + (4/3)

4x + 13 = (2x/3) + (4/3)

4x - (2x/3) = (4/3) - 13

(10x/3) = (-35/3)

10x = -35

x = -3.5

y = 4x + 13

y = (4×-3.5) + 13 = -14 + 13 = -1

coordinates of the orthocentre of the triangle = (-3.5, -1)

Hope this Helps!!!

6 0
3 years ago
Need help, this is 7th grade, will be 50 points for work shown
Vikki [24]

Answer:

.111      11.1%

2/5        2:5

12.5%        1:8

Step-by-step explanation:

3 0
3 years ago
a stadium floor that is in the shape of a circle has a diameter with a length of 210 yards which of these measurements is closes
Grace [21]
Area  = 3.14 * radius^2

Here we have area = 3.14 * 105^2 =  34,618.5  yd^2
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Help a brother out #2
valentinak56 [21]

Answer:

He is αβ 60° and 30° i need some in my answers 5 brain list answers

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I need help fast like rn
lbvjy [14]

Answer:

vyuWYIRTG3ñwyiehg

Step-by-step explanation:

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