Find the area of a triangle and show your work. The triangle has following formulas: y=3x-1, y=1/2x-2, y=-4x+5?
Find the area of a triangle and show your works. The triangle has following formulas:
y=3x-1
y=1/2x-2
y=-4x+5
That’s a LONG problem. I can explain what you need to do, step by step.
1. Find the points of intersection of the lines (this will give you the 3 vertices of your triangle). To do that, take the equations 2 at a time and use substitution or elimination to solve. First take the 1st two, then the bottom two, then the 1st and 3rd.
Example: the 1st two:
y=3x-1
y=1/2x-2
Substitute to get:
3x – 1 =1/2x – 2 Multiply everything by 2:
6x – 2 = x – 4 Subtract x from each side:
5x – 2 = -4 Add 2 to each side:
5x = -2 Divide each side by 5
x = -2/5
Find y: y = 3x – 1 = 3(-2/5) – 1 = -6/5 – 1 = -11/5
So the first point is (-2/5, -11/5)
Do that for the remaining pairs of lines.
2. Pick what side you want your base to be. Use the distance formula to find out how long that side is.
d = √[(x2 - x1)^2 + (y2 - y1)^2 ]
3. Find the equation of the line that’s perpendicular to your base and goes through the opposite vertex (that’ll be your altitude).
4. Find the point of intersection between your altitude and your base. (Using the same method as in the 1st step).
5. Find the length of your altitude using the distance formula (endpoints are the vertex opposite the base and the point of intersection you found in step 4).
6. Area of a triangle is 1/2(bh)
1
References :
That’s a LONG problem. I can explain what you need to do, step by step.
1. Find the points of intersection of the lines (this will give you the 3 vertices of your triangle). To do that, take the equations 2 at a time and use substitution or elimination to solve. First take the 1st two, then the bottom two, then the 1st and 3rd.
Example: the 1st two:
y=3x-1
y=1/2x-2
Substitute to get:
3x – 1 =1/2x – 2 Multiply everything by 2:
6x – 2 = x – 4 Subtract x from each side:
5x – 2 = -4 Add 2 to each side:
5x = -2 Divide each side by 5
x = -2/5
Find y: y = 3x – 1 = 3(-2/5) – 1 = -6/5 – 1 = -11/5
So the first point is (-2/5, -11/5)
Do that for the remaining pairs of lines.
2. Pick what side you want your base to be. Use the distance formula to find out how long that side is.
d = √[(x2 - x1)^2 + (y2 - y1)^2 ]
3. Find the equation of the line that’s perpendicular to your base and goes through the opposite vertex (that’ll be your altitude).
4. Find the point of intersection between your altitude and your base. (Using the same method as in the 1st step).
5. Find the length of your altitude using the distance formula (endpoints are the vertex opposite the base and the point of intersection you found in step 4).
6. Area of a triangle is 1/2(bh)
References :