1.Find the area of the convex quadrilateral with vertices (1, 5), (2, 3), (7, 6) and (7, 1).
2.A line goes through (2, 3) and (−8,−2). The line has an x-intercept of P and a y-intercept of Q. Let the origin be O. Find the area of OPQ
3.The point (−3, 2) is rotated 90◦ clockwise around the origin to point B. Point B is then reflected in the line y = x to point C. What are the coordinates of C?
+773 only post one or two questions at a time like Melody says, please, and don't say help for school homework, that just means you are trying to cheat:(
+1005 Read CPhill's.
However I got 19 as my answer.
Top triangle 6*1, left 1*2, center rectangle 2*5 and bottom triangle 5*2, so we have
3+1+10+5 = 19.
+1005 
So I graphed the line, in red. The x intercept is -4 and the y intercept is 2. SO we have a triangle of base 4 and height 2. The triangle is 4*2/2 = 4 units.
+1005 
So we have that.
If we turn it 90 degrees clockwise we have the rectangle with a point at (2,3).
If you don't understand anything feel free to ask!
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Edited by: Me!
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+23245 Question #1: On graph paper:
-- plot point A(1,5)
-- plot point B(7,6)
-- plot point C(7,1)
-- plot point D(2,3)
Connect sides AB, BC, CD, and DA to get the quadrilateral ABCD.
Now, find point E(7,5) and point F(7,3).
Draw a line segment from A to E and another line segment from D to F.
Quadrilateral ABCD is now divided into a top triangle (ABE), a bottom triangle (DFC)
and a middle trapezoid.
If we find the areas of these three figures and add them together, we will have the area
of quadrilateral ABCD.
To get the area of the top triangle (ABE):
-- the base is AE (find this length)
-- the height is EB (find this length)
-- and use the formula: A = ½ · base · height = .........
To get the area of the bottom triangle (DFC)
-- the base is DF (find this length)
-- the height is FC (find this length
-- and use the formula: A = ½ · base · height = .........
To get the area of the trapezoid (AEFD)
-- one of the bases is FD
-- the other base is EA
-- the height is EF
-- and use this formula: A = ½ · h · (base1 + base2) = .........
Now, add these areas together to get the total area ....
+128475 1.Find the area of the convex quadrilateral with vertices (1, 5), (2, 3), (7, 6) and (7, 1).
See the image here
We can use something known as Pick's Theorem to solve this
Note...a lattice point = a point with integer coordinates
Area = number of boundary lattice points /2 + number of interior lattice points - 1 =
(4/2) + 16 - 1 =
2 + 16 - 1 =
17
