Westonci.ca offers fast, accurate answers to your questions. Join our community and get the insights you need now. Get immediate and reliable answers to your questions from a community of experienced experts on our platform. Get immediate and reliable solutions to your questions from a community of experienced professionals on our platform.
Sagot :
The equations of the three altitudes of triangle ABC include the following:
- 3y - 2y - 4 = 0.
- y + 3x - 8 = 0.
- 4y + x - 6 = 0.
What is a triangle?
A triangle can be defined as a two-dimensional geometric shape that comprises three (3) sides, three (3) vertices and three (3) angles only.
What is a slope?
A slope is also referred to as gradient and it's typically used to describe both the ratio, direction and steepness of the function of a straight line.
How to determine a slope?
Mathematically, the slope of a straight line can be calculated by using this formula;
[tex]Slope, m = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope, m = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]
Also, the point-slope form of a straight line is given by this equation:
y - y₁ = m(x - x₁)
Assuming the following parameters for triangle ABC:
- Let AM be the altitudes on BC.
- Let BN be the altitudes on CA.
- Let CL be the altitudes on AB.
For the equation of altitude AM, we have:
Slope of BC = (2 - 8)/(4 - 0)
Slope of BC = -6/4
Slope of BC = -3/2
Slope of AM = -1/slope of BC
Slope of AM = -1/(-3/2)
Slope of AM = 2/3.
The equation of altitude AM is given by:
y - y₁ = m(x - x₁)
y - 0 = 2/3(x - (-2))
3y = 2(x + 2)
3y = 2x + 4
3y - 2y - 4 = 0.
For the equation of altitude BN, we have:
Slope of CA = (2 - 0)/(4 - (-2))
Slope of CA = 2/6
Slope of CA = 1/3
Slope of BN = -1/slope of CA
Slope of BN = -1/(1/3)
Slope of BN = -3.
The equation of altitude BN is given by:
y - y₁ = m(x - x₁)
y - 8 = -3(x - 0)
y - 8 = -3x
y + 3x - 8 = 0.
For the equation of altitude CL, we have:
Slope of AB = (8 - 0)/(0 - (-2))
Slope of AB = 8/2
Slope of AB = 4
Slope of CL = -1/slope of AB
Slope of CL = -1/4
The equation of altitude CL is given by:
y - y₁ = m(x - x₁)
y - 2 = -1/4(x - 4)
4y - 2= -(x - 4)
4y - 2= -x + 4
4y + x - 2 - 4 = 0.
4y + x - 6 = 0.
In conclusion, we can infer and logically deduce that the equations of the three altitudes of triangle ABC include the following:
- 3y - 2y - 4 = 0.
- y + 3x - 8 = 0.
- 4y + x - 6 = 0.
Read more on point-slope form here: brainly.com/question/24907633
#SPJ1
We appreciate your time. Please revisit us for more reliable answers to any questions you may have. Thank you for visiting. Our goal is to provide the most accurate answers for all your informational needs. Come back soon. Westonci.ca is your trusted source for answers. Visit us again to find more information on diverse topics.