Geometry help?

Question

Can someone help me do these 3 problems by showing step by step how to find the area?

Draw the figure in a coordinate plane and find it's area.

1. Triangle defined by A (3,4), B (7, 4), and C(5, 7).

2. Triangle defined by R(-2, -3), S (6, -3), and T (5,4).

3. Triangle defined by L(-2, -4), M (-2, 1), N (7,1), and P(7, -4).

Any help would be greatly appreciated.

I understand how to graph the points, I'm just not sure how to find the area.
Do I use the distance formula with all of the sides and then use the area forumula?

Answer 1

The formula for area of a 2 dimensional triangle using co-ordinates is as follows:
for a triangle represented by the coordinates
A(X1, Y1), B(X2, Y2) and C(X3, Y3) is given by
1/2(-X2Y1 + X3Y1 + X1Y2 - X3Y2 - X1Y3 + X2Y3)
using this formula we can easily calculate the given hre
for eg.
A(3, 4), B(7, 4) and C(5, 7)
Area = 1/2(-7*4 + 5*4 + 3*4 - 5*4 - 3*7 + 7*7)
Therefore
Area = 1/2(-28 +20 + 12 - 20 - 21 +49)
Area = 1/2 * 12 = 6 units
please use this formula remembering that the value in the bracket is taken as absolute.
The 3rd triangle is not a triangle having 4 co-ordinate vertex points.

Answer 2

1. A(3, 4), B(7, 4), C(5, 7)

First label each of the co-ordinate pairs:
A(x1 = 3, y1 = 4)
B(x2 = 7, y2 = 4)
C(x3 = 5, y3 = 7)

Area, A = 1/2 x base x height, or
A = 1/2bh

Notice that on Side A→B, y1 = y2. That means the side is horizontal, so the length, or base of the triangle, is simply x2 - x1:
b = 7 - 3
b = 4

h = y3 - y1
h = 7 - 4
h = 3

A = 1/2bh
A = 1/2(4)(3)
A = 6 sq. units
¯¯¯¯¯¯¯¯¯¯¯¯

2. Do the same thing here. Notice that y1= y2, so that side is horizontal . Use it as the base and solve.

3. Only 3 pts. on a graph for a triangle. Disregarding pt. P, solve the same way.

Answer 3

1. Triangle ABC line AB is 4 units long and horizontal ( same, y coordinate ) Line (5,7) goes up 3 and is 2 units from point a or point B. Area of a triangle is 1/2 Base x height
AREA = 6 Sq. Units

2. from r to s is 8 units and horizontal same y different x coordinates Height is 7 distance in y's from -3 to positive 4
7 units

Area of a triangle is 1/2 Base x height
AREA = 28 Sq. Units

3. # 3 has 4 points and I believe it's a rectangle thats 9x5 for and area of 45 sq units.

Answer 4

there is a formula for finding area of triangle just by having the coordinates. ask your teacher or look up books.

.....l3 7 5 3l
A=l4 4 7 4l

it looks like this somehow.

Answer 5

There's no way to explain how to draw it. Here, watch me while I draw it.

See what I mean? And until you draw them, you're probably not going to see how to get the area.

You CAN find the area just by knowing those points, but I probably couldn't explain it to you without writing a lot more than this box lets me. :)