Given triangle XYZ with vertices
X(-2,0),Y(6,0), and Z(4,8), find the number of square units in its area.
Since two points lie on the x-axis, this becomes an easy question
Consider XY as the base, its length would be 8
Z is 8 units above the x-axis, so the height is 8
Area = (1/2)base x height
= (1/2)(8)(8) = 32
To find the area of a triangle with given vertices, you can use the formula for the area of a triangle:
Area = (1/2) * base * height
In this case, we have the vertices X(-2,0), Y(6,0), and Z(4,8). To find the base and height, we can take any two points from the vertices and calculate the distance between them.
Let's take points X(-2,0) and Y(6,0) as the base. The distance between these two points (base) is:
Base = X-coordinate of Y - X-coordinate of X
= 6 - (-2)
= 6 + 2
= 8
Now, let's find the height. We can take either the distance between point Z(4,8) and point X(-2,0) or the distance between point Z(4,8) and point Y(6,0).
Height = Y-coordinate of Z - Y-coordinate of X
= 8 - 0
= 8
The base and height values we found are 8 and 8, respectively. Now, we can calculate the area using the formula:
Area = (1/2) * base * height
= (1/2) * 8 * 8
= 4 * 8
= 32 square units
Therefore, the area of triangle XYZ is 32 square units.