Question

http://www.nysedregents.org/Geometry/20100818-geo-exam.pdf i need help with the last two part 3 questions

Answer 1

I cant help you wif question 36, because i dont' understand the notation D 2 . T 3,-2. I have never seen that before. Although i didnt learn much geometry, but i dont think it is a hard question.

As for question 37, it is solved as such.

Form a system of equations for a and b

a +b = 5

As for the second equation, for it by equating h together.

3^2 - b^2 = h^2 = 4^2 - a^2

9- b^2 = 16 - a^2

Since a+b = 5, a = 5-b

9- b^2 = 16 - (5-b)^2
9- b^2 = 16 - (25 - 10b + b^2)
9 - b^2 = 16 - 25 +10b - b^2
18 = 10 b
b = 18/10 = 1.8

With b found, you can find h.

3^2 - b^2 = h^2
9- 1.8 ^2 = h^2
9- 3.24 = h^2
h^2 = 5.76
h= 2.4

Answer 2

If you do know of the composite transformation, you can tell me more, then i can help you if deem fit.

Answer 3

I need question 38 actually . thank you for 37!

Answer 4

Give me a moment for 38.

Answer 5

Okay. Note that a parallelogram has 2 pairs of parallel sides. A rhombus also has 2 pairs of parallel sides, but they are all of same length. A rectangle also has 2 pairs of parallel sides, but the angles are all right angles. So to prove that ABCD is a parallelogram and not a rhombus or a rectangle, we have to find 2 proofs, It does not have equal sides, and it does not have a right angle.


So first go on to prove ABCD is a parallelogram by finding the gradient of AB and CD, they should be equal. And then do the same for AC and BD, they should be equal also.

Now that you prove it is a parallelogram, go on to prove it is not a rhombus. Find the length from the point AB and the length of CD, once they are not equal, it is considered proven alrdy, not need to go on to find AC and BD.

Then go on to find one angle, anyone. As long it is not 90, it is enough. As you already proven 2 pairs or parallel sides, impossible to have one only one side at right angles. Once one side is right angle, all sides have to be right angles.

If you don't know the exact mathematics, just let me know. This is just a general explanation as to how to gou about the question.

Answer 6

for the 37 in the second equation why are they minus signs between each ter, in the 2nd equation ( 3^2 and b^2...=h^2+..)

Answer 7

term*

Answer 8

3^2 - b^2 = h^2 = 4^2 - a^2

It is in this form because in both triangles 3 and 4 are the hypotenuse ( the longer side). So to find the side of h, 3^2 - b^2. As given in Pythagorus theorum

Answer 9

9- b^2 = 16 - (25 - 10b + b^2)
9 - b^2 = 16 - 25 +10b - b^2
why does it change to negative between 10b and b^2

Answer 10

oh because of the bracket (25 - 10b + b^2)

The minus sign before the bracket, will change the signs of the terms in the brackets when expanded out. I didnt skip that step, to provide clarity and prevent carelessness.

Answer 11

can u prove their lengths through units of the graph?

Answer 12

Yes you can do so via the graph, even the angles portion can be done with the graphs.

Answer 13

ok so i got as far as proving its not a rhombus but i dont know how to prove the angles

Answer 14

Okay if you are using the graph method, by plotting out the points, it can be easily shown it is not a right angle as it does not fit into the squares of the graph at all.

Another simpler method, instead of finding the value of the angle, is to just find the gradient of the 2 lines, AB and BC. If those gradients are not perpendicular to each other, there is no right angle.