Geometry HELP!!!!!!?

Question

I need help on these problems for a geometry packet. Please tell me HOW you did it along with the answers if you can. Thanks a lot!!

1. There is a long rectangle with 8 verticle lines going through it. How many rectangles are in the figure?

2. Point P(3,2) is on a line which is parallel to the line x-3y=7. What is the equation of the line?

3. There is a pentagon with a star inside touching all 5 corners of the pentagon. How many triangles are in the diagram?

Answer 1

Sorry but the last two answers for the first question are incorrect. We can take the width as 1 unit.

Here there are 9 rectangles with length1,8 rectangles with length 2,...,and 1 rectangle with length 1. Thus, total number of rectangles in this grid is 9+8+...+1=45 .

Answer 2

1. 9 <= just draw the picture and it's easy to see



2. parallel means equal slopes. solve 1st eq for y.

x-7 = 3y

x/3 - 7/3 = y

slope: 1/3



y = x/3 + c <= plug in (3,2) to find c

2 = 3/3 + c

2 = 1 + c

c = 1



Final eq: y = x/3 + 1



3. Again, draw the picture. It depends on if the star is drawn with lines in the middle of the star. If it is, there are 11 triangles. If not, there are only the 5 outside the star.

Answer 3

Be careful with number 1. It's not as easy as the others make it seem. Draw the picture. The initial rectangle is #1. Then you have the 9 rect. inside the initial one. So now you have 9 +1 = 10 rects. Now, look at the 9 rects. inside the bigger one. Every two of those rects. make up another, different rect. So you have 8 rects. that consist of two smaller rects on the inside. Now look at the ones that are 3 of the smaller rects. on the inside of the big one. These are once again different rects and there are 7 of these. There are 6 ones that are four small rects across. There are 5 that are 5 small rects across. There are 4 that are 6 small rects. across, and there are 3 that are 7 small rects across. And finally you have 2 that are 8 small rects. Add them all up and you get 9+8+7+6+5+4+3+2+1 = 45

Answer 4

1. if you put one verticle line into a rectangle, you get two rectangles. If you add one more line, you get three. If you add another, you get four rectangles.... So the number of lines you add + 1 = number of rectangles.



0 verticle lines = 1 rectangle

8 verticle lines = 9 rectangles

Answer 5

2. graph the equation first. x-3y=7.-3y=-x+7. y= (x/3) - (7/3) [okay that's gonna be kinda hard to graph]. then graph the point. parallel lines have the same slope but different y-intercecpts, so you need to kinda mess around with your equation and find the right y-intercecpt.



for 1 and 3, take your time and count. use color pencils to make sure you count each one.