What is the area, in square units, of a triangle whose vertices are at (4,-1), (10,3) and (4,5) ?
How to do this?
It helps if you plot the points first, then you can find the length of the sides of the triangle.
area of a triangle is
1/2 base times height.
http://www.algebra.com/algebra/homework/Triangles/Triangles.faq.question.461705.html
ok thanks
I could also i think find the area of the square/rectangle and minus the pieces that are not part of the triangle
Knights, If you are in analytic geometry, I am pretty certain your teacher expects an analytical approach, not a graphical approach. See the example I posted.
To find the area of a triangle with given vertices, you can use the formula for the area of a triangle using coordinates. The formula is known as the Shoelace Formula or the Gauss's Area Formula.
Here are the steps to find the area of a triangle using the Shoelace Formula:
1. Write down the coordinates of the three vertices of the triangle. Let's label them as A (4,-1), B (10,3), and C (4,5).
2. Write down the coordinates of vertex A twice to the right. It will look like this: A B C A.
3. Write down the y-coordinates of the vertices from step 1 in the same order, but in reverse. It will look like this: -1 3 5 -1.
4. Multiply each x-coordinate from step 2 by the corresponding y-coordinate from step 3.
5. Multiply each y-coordinate from step 2 by the x-coordinate to its left from step 3.
6. Take the sum of the products from steps 4 and 5.
7. Divide the sum calculated in step 6 by 2. The absolute value of this result will give you the area of the triangle (since the result can be negative due to the subtraction of two areas).
Let's go through the steps using the given coordinates:
1. The coordinates are A (4,-1), B (10,3), and C (4,5).
2. A B C A.
3. -1 3 5 -1.
4. (4 * 3) + (10 * 5) + (4 * -1) = 12 + 50 - 4 = 58.
5. (-1 * 10) + (3 * 4) + (5 * 4) = -10 + 12 + 20 = 22.
6. 58 - 22 = 36.
7. The absolute value of 36/2 is 18.
Therefore, the area of the triangle with vertices (4,-1), (10,3), and (4,5) is 18 square units.