Find the area of the triangle defined by the coordinates (-3, -4), (-7, 0), and (-3, 4).
To find the area of a triangle defined by three coordinates, we can use the formula for the area of a triangle using coordinates.
The formula for the area of a triangle given three coordinates (x1, y1), (x2, y2), and (x3, y3) is:
Area = 1/2 * |x1(y2 - y3) + x2(y3 - y1) + x3(y1 - y2)|
Let's calculate the area using the given coordinates (-3, -4), (-7, 0), and (-3, 4).
x1 = -3
y1 = -4
x2 = -7
y2 = 0
x3 = -3
y3 = 4
Now we can substitute these values into the formula and calculate the area:
Area = 1/2 * |-3(0 - 4) + (-7)(4 - (-4)) + (-3)((-4) - 0)|
Area = 1/2 * |-12 + (-7)(8) + (-3)(-4)|
Area = 1/2 * |-12 - 56 + 12|
Area = 1/2 * |-56|
Area = 1/2 * 56
Area = 28 square units
Therefore, the area of the triangle defined by the coordinates (-3, -4), (-7, 0), and (-3, 4) is 28 square units.
To find the area of a triangle defined by three coordinates, you can use the Shoelace Formula.
1. First, write down the coordinates of the three points.
Point A: (-3, -4)
Point B: (-7, 0)
Point C: (-3, 4)
2. List the x-coordinates of the three points in a column from left to right.
x: -3, -7, -3
3. List the y-coordinates of the three points in a column from top to bottom.
y: -4, 0, 4
4. Multiply each x-coordinate with the y-coordinate below it and write the products in a new column to the right. Repeat this for all the points.
x*y: (-3 * 0) = 0
(-7 * 4) = -28
(-3 * -4) = 12
5. Multiply each y-coordinate with the x-coordinate to its right and below it and write the products in a new column to the right. Repeat this for all the points.
y*x: (-4 * -7) = 28
(0 * -3) = 0
(4 * -3) = -12
6. Add up the products in each column.
Sum of x*y = 0 + (-28) + 12 = -16
Sum of y*x = 28 + 0 + (-12) = 16
7. Take the absolute value of the difference between the sums.
|Sum of x*y - Sum of y*x| = |-16 - 16| = 32
8. Divide the absolute value obtained in step 7 by 2 to find the area of the triangle.
Area = 32 / 2 = 16 square units
Therefore, the area of the triangle defined by the coordinates (-3, -4), (-7, 0), and (-3, 4) is 16 square units.
What method have you learned.
There are multiple ways to answer the question,
e.g. Heron's formula etc