The vertices of a triangle are (-2,3),(2,1) and (2,7). What is the area of this triangle?
Two vertices are on the same vertical line, namely x=2, for (2,1) and (2,7).
This is the base of the triangle with length 7-1=6.
The height of the triangle from point (-2,3) to x=2 is 2-(-2)=4.
Area of triangle
= (1/2)base*height
= (1/2)6*4
= 12
Well, I hope you're ready for a triangle-tastic explanation! To find the area of a triangle, we can use the formula:
Area = 1/2 * base * height
Now, our first step is to find the base and height of the triangle. We can do this by using the given vertices as our clues.
Looking at the vertices (-2,3),(2,1), I can't help but think this triangle is feeling a bit tipsy. It's like it's leaning towards a life of adventure! But let's get back to business.
The base of the triangle is the distance between (-2,3) and (2,1). Using some distance formula magic, we can calculate the base:
(base) = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(2 - (-2))^2 + (1 - 3)^2]
= √[4^2 + (-2)^2]
= √[16 + 4]
= √20
= 2√5
So now we know the base of our triangle is 2√5. It has a base on the move!
The height of the triangle is the distance between (2,1) and (2,7). Let's calculate the height using the distance formula once again:
(height) = √[(x2 - x1)^2 + (y2 - y1)^2]
= √[(2 - 2)^2 + (7 - 1)^2]
= √[0^2 + 6^2]
= √(0 + 36)
= √36
= 6
Alrighty, we now have both the base and height of our triangle! The base is 2√5 and the height is 6. Let's plug these values into the area formula:
Area = 1/2 * base * height
= 1/2 * (2√5) * 6
= √5 * 6
= 6√5
So, the area of this triangle is 6√5. Don't you dare underestimate the adventurous spirit of this leaning triangle! It's got quite the captivating area, don't you think?
To find the area of a triangle given the coordinates of its vertices, you can use the formula for the area of a triangle using coordinates:
Area = |(x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)) / 2|
Let's calculate the area step-by-step:
1. Assign the coordinates of the vertices:
A(x1, y1) = (-2, 3)
B(x2, y2) = (2, 1)
C(x3, y3) = (2, 7)
2. Calculate the expression inside the absolute value:
|(-2(1 - 7) + 2(7 - 3) + 2(3 - 1)) / 2|
Simplifying the expression:
|(-2(-6) + 2(4) + 2(2)) / 2|
Simplifying further:
|(12 + 8 + 4) / 2|
|24 / 2|
|12|
3. Take the absolute value of the result:
Area = 12
Therefore, the area of the triangle with vertices (-2,3), (2,1), and (2,7) is 12 square units.
To find the area of a triangle given the coordinates of its vertices, you can use the formula for the area of a triangle using coordinates. The formula is:
Area = 0.5 * |(x1(y2-y3) + x2(y3-y1) + x3(y1-y2))|
Let's substitute the given coordinates into the formula:
x1 = -2, y1 = 3
x2 = 2, y2 = 1
x3 = 2, y3 = 7
Now we can calculate the area of the triangle.