Given (2, 3), (4, 5), (6, 7), find the area using the formula below.
Note: (a, b) (c, d) (e, f)
a = 2
b = 3
c = 4
d = 5
e = 6
f = 7
A = (1/2)[(ad - cb) + (cf - ed) + (eb - af)]
MarkFL said:Suppose you weren't given a formula into which you may "plug and chug"...can you outline a method you could use to find the area?
RTCNTC said:1. Apply distance formula 3 times.
2. Heron's Formula.
The formula for finding the area of a triangle given three coordinate points is (1/2) * base * height, where the base is the distance between any two of the given points and the height is the perpendicular distance from the third point to the base.
To calculate the base, you need to find the distance between any two of the given points. This can be done using the distance formula, which is √((x2-x1)^2 + (y2-y1)^2), where (x1,y1) and (x2,y2) are the coordinates of the two points. To calculate the height, you need to find the perpendicular distance from the third point to the base. This can be done by finding the slope of the base and using the formula for the distance from a point to a line, which is |ax0 + by0 + c| / √(a^2 + b^2), where (x0,y0) is the coordinate of the third point and the line is represented by the equation ax + by + c = 0.
Yes, as long as the three points are not collinear (lying on the same line), you can use them to find the area of a triangle using the formula (1/2) * base * height.
There is no set rule for deciding which two points to use for the base and which point to use for the height. However, it is usually easier to calculate the distance between two points that have coordinates with smaller values, as it involves smaller numbers and simpler calculations. You can also choose points that seem to form a right angle, as it can make calculating the height easier.
The unit of measurement for the area of a triangle depends on the unit of measurement used for the coordinates. If the coordinates are given in units of length (such as meters or centimeters), then the area will be in square units (such as square meters or square centimeters). If the coordinates are given in units of degrees, then the area will be in square degrees.