area of triangle with following coordinates?

Question

find the area of the triangle with coordinates (0,8) (4,4) (0,-2) i hope u elaborate on how i totally forgot how to do it and thanks to all

Answer 1

Plot points A(0,8), B(0,-2), C(4,4)
CE is perpendicular to AB
Area = (1/2) AB x CE
Area = (1/2) (10) (4)
Area = 20 units²

Answer 2

Ok, it might help if you drew this out on the coordinate plane.

Let's name the points (to make it easier to explain).
A = (0, 8)
B = (4, 4)
C = (0, -2)

I'm going to make AC the base of the triangle. (Remember - area = 1/2 * base * height)

We need to find the length of AC.
distance = sqrt [(0 - 0)^2 + (8 - -2)^2]
= sqrt [0 + 10^2)
= sqrt 100
= 10

Now, we need the "height" of the triangle.
The "height" will be a line from point B to segment AC that's perpendicular to AC. Since AC is on the y-axis, the "height" of the triangle will be the horizontal distance from the y-axis to point B.
the y-axis x-value is 0. The point B x-value is 4. So the "height" of the triangle is 4 - 0 = 4.

So,

Area = (1/2)(AC)(height)
= (1/2)(10)(4)
= 20

Answer 3

It is a mental arithmetic.
How to do it?

Two of your points have x=0 (same). and y difference is 10. It implies said two points when joined it is a horizontal line...(1)

Next point of triangle is 4, 4. It shows "vertical distance from this point to horizontal line (1)" is 4.

So triangle lies with in a rectangle of 10*4

Triangle area 1/2 rectangle area that inscribe triangle which is equal to 40/2 (say 20 square units)!

So it is a mental arithmetic!

Answer 4

Here's a cool way:

If the coordinates of the vertices are (x1,y1), (x2,y2), and (x3,y3), then the area is given by the formula

A = (1/2) det[(x1,y1,1), (x2,y2,1), (x3,y3,1)].

Try it; it works! For a proof, just put a fourth point in the plane so as to make a parallelogram, and use the fact that the area of a parallelogram is base*height.

Answer 5

Graph the points on a coordinate axis. When graphed it is clear that we can consider the base of the triangle on the y-axis b=10
the height is the distance from the y-axis to the point (4,4)
h =4
I will leave it to you to finish the problem.

Answer 6

The area of triangle formed by the coordinates (x1, y1),

(x2, y2), (x3, y3) is given by

A = 1/2[x1(y2-y3) + x2(y3-y1) + x3(y1 - y2)]

here x1 = 0, x2 = 4, x3 = 0

y1 = 8, y2 = 4, y3 = -2

=1/2[0(4+2) + 4(-2 - 8) + 0(8-4)]

= 1/2(4(-10)

= -20

= 20 sq.units ignoring negative sign

Answer 7

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area of triangle with following coordinates?
find the area of the triangle with coordinates (0,8) (4,4) (0,-2) i hope u elaborate on how i totally forgot how to do it and thanks to all