The base length of the triangle with vertices A(1,1, B(9,1), C(5,5)is multipliend by 2.Describe the effect of the change on the area.
can someone help me on this one.. am stuck
When the base length of a triangle is multiplied by 2, the effect on the area of the triangle depends on whether the height of the triangle remains the same.
To determine the effect, we need to calculate the area of the original triangle and the area of the new triangle with the doubled base length.
First, let's find the original area of the triangle using the formula:
Area = (1/2) * base * height
The base of the original triangle is the distance between points A(1,1) and B(9,1) = 9 - 1 = 8 units.
To find the height, we need a perpendicular line from vertex C(5,5) to the base.
The slope of the base is (1 - 1) / (9 - 1) = 0, so a perpendicular line will have a slope of undefined.
Using the point-slope form of a line, we can write the equation of the perpendicular line passing through C(5,5):
y - 5 = undefined * (x - 5)
Since the slope is undefined, the equation simplifies to x = 5.
Now, we can find the height of the original triangle by measuring the perpendicular distance between C(5,5) and the line x = 5.
The height is the distance between points C(5,5) and (5,1), which is 5 - 1 = 4 units.
Now, we can calculate the original area:
Area = (1/2) * base * height
= (1/2) * 8 * 4
= 16 square units
Next, let's calculate the new area after doubling the base length.
The new base length is 2 times the original base length, so it becomes 2 * 8 = 16 units.
Now we need to check if the height remains the same. Since the height was perpendicular to the original base, it will still be perpendicular to the new base. Therefore, the height remains the same at 4 units.
Now, we can calculate the new area:
Area = (1/2) * new base * height
= (1/2) * 16 * 4
= 32 square units
Comparing the original area (16 square units) and the new area (32 square units), we can see that the area is doubled when the base length is multiplied by 2.
Therefore, when the base length of the triangle is multiplied by 2, the area of the triangle is increased by a factor of 2.
Sure, I can help you with that!
To describe the effect of the change on the area of the triangle, we first need to calculate the area of the original triangle. Then we can multiply the base length by 2 and calculate the area of the new triangle. Finally, we can compare the two areas to determine the effect of the change.
Let's start by finding the base length of the original triangle. The base length is the distance between the vertices A(1, 1) and B(9, 1). We can use the distance formula to calculate it:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates, we get:
Distance = sqrt((9 - 1)^2 + (1 - 1)^2)
= sqrt((8)^2 + (0)^2)
= sqrt(64 + 0)
= sqrt(64)
= 8
So, the base length of the original triangle is 8 units.
Now, let's calculate the area of the original triangle. We can use the formula for the area of a triangle, which is:
Area = (1/2) * base * height
Since the base length is 8, we need to find the height. The height is the distance between the base and the third vertex of the triangle, which is C(5, 5). We can calculate it using the distance formula again:
Height = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Substituting the coordinates, we get:
Height = sqrt((5 - 5)^2 + (5 - 1)^2)
= sqrt((0)^2 + (4)^2)
= sqrt(0 + 16)
= sqrt(16)
= 4
So, the height of the original triangle is 4 units.
Now, we can calculate the area:
Area = (1/2) * base * height
= (1/2) * 8 * 4
= 16
Therefore, the area of the original triangle is 16 square units.
Next, we need to multiply the base length by 2 to find the new base length. 2 times 8 gives us 16.
Now that we have the new base length, we can calculate the area of the new triangle using the same formula:
Area = (1/2) * base * height
Since the new base length is 16, we need to find the height. The height remains the same because it is the distance between the base and the third vertex, which has not changed.
So, the height of the new triangle is still 4 units.
Now, let's calculate the area:
Area = (1/2) * base * height
= (1/2) * 16 * 4
= 32
Therefore, the area of the new triangle is 32 square units.
Comparing the areas, we can see that the area of the original triangle was 16 square units, while the area of the new triangle is 32 square units.
So, by multiplying the base length by 2, the area of the triangle is also multiplied by 2. This tells us that the change has made the new triangle twice as large as the original triangle.
A = (b/2) *h,
Multiply the base by 2 and get:
A = b*h,
So the area is doubled.
Let's calculate the area of the given
triangle.
A(1,1), B(9,1), C(5,5).
AB = 9 - 1 = 8 = base.
(AC)^2 = (5-1)^2 + (5-1)^2,
(AC)^2 = 16 + 16 = 32,
AC = sqrt32 = 5.66.
(b/2)^2 + h^2 = (AC)^2,
4^2 + h^2 = 32,
h^2 = 32 - 16 = 16,
h = 4.
A = (b/2) * h,
A = (8/2) * 4 = 16.
Double the base:
A = (16/2) * 4 = 32.