Question

An architect plans to make a drawing of the room of a house. The segment LM represents the ceiling of the room. He wants to construct a line passing through Q and perpendicular to side LM to represent a wall of the room. He uses a straightedge and compass to complete some steps of the construction, as shown below:

Answer 1

Which of these is likely to be his next step in constructing the perpendicular line?

Fix the compass at Q, and draw an arc below the line.
Fix the compass at L, and draw an arc above the line.
Without changing the width, and position of the compass, draw an arc between L and M.
Without changing the width of the compass, place the compass at M, and draw an arc.

Answer 2

@Will.H please help me

Answer 3

i think it's either A or C but I'm not 100% sure

Answer 4

it can't be C as drawing an arc positioned between L and M won't make a perpendicular line!

Answer 5

so then a right?

Answer 6

yeah

Answer 7

yay thanks for confirming! (:

Answer 8

i have another one i need help/confirmation on if ur not busy

Answer 9

my pleasure :)

Answer 10

sure

Answer 11

theres 3 more only that i need the confirmation/help on

Answer 12

Oki

Answer 13

Look at the right triangle ABC below:

Answer 14

A student made the following chart to prove that AB2 + BC2 = AC2:


Statement Justification
1. Triangle ABC is similar to triangle BDC 1. Angle ABC = Angle BCD and Angle BCA = Angle DBC
2. BC2 = AC x DC 2. BC ÷ DC = AC ÷ BC because triangle ABC is similar to triangle BDC
3. Triangle ABC is similar to triangle ABD 3. Angle ABC = Angle ADB and Angle BAC = Angle DAB
4. AB2 = AC x AD 4. AB ÷ AD = AC ÷ AB because triangle ABC is similar to triangle ADB
5. AB2 + BC2 = AC x AD + AC x DC = AC (AD + DC) 5. Adding Statement 1 and Statement 2
6. AB2 + BC2 = AC2 6. AD + DC = AC

What is the flaw in the student's proof?
Justification 4 should be "AB ÷ AD = AB ÷ AC because triangle ABC is similar to triangle ABD."
Justification 1 should be "Angle ABC = Angle BDC and Angle BCA = Angle DCB."
Justification 2 should be "BC ÷ DC = BC ÷ AC because triangle ABC is similar to triangle BDC."
Justification 3 should be "Angle ABC = Angle BAD and Angle BAC = Angle ABD."

Answer 15

i say the answers C

Answer 16

but I'm nostrum if the answers c or maybe a?

Answer 17

not sure*

Answer 18

Justification 1 should be "Angle ABC = Angle BDC and Angle BCA = Angle DCB."
because they both right angles

Answer 19

so the answers not C?

Answer 20

you think its b?

Answer 21

am certain

Answer 22

you're certain its B? because i need to pass this class

Answer 23

yup

Answer 24

okay so 2 more

Answer 25

shoot

Answer 26

Kite ABCD is reflected over the line y = x. What rule shows the input and output of the reflection, and what is the new coordinate of A'?

Answer 27

(x, y) → (y, x); A' is at (2, −7)
(x, y) → (−x, y); A' is at (7, 2)
(x, y) → (−x, −y); A' is at (7, −2)
(x, y) → (y, −x); A' is at (2, 7)

Answer 28

i think C, yes?

Answer 29

(x,y) --> (y,x)
that's the rule of reflection across y=x
A(-7,2) --> A'(2,-7)

so it's A

Answer 30

oh ok makes sense

Answer 31

Rectangle ABCD is reflected over the x-axis, followed by a reflection over the y-axis, and then rotated 180 degrees about the origin. What is the location of point A after the transformations are complete?

Answer 32

(−5, 1)
(5, −1)
(−5, −1)
(5, 1)

Answer 33

I say D, yes?

Answer 34

A?

Answer 35

I think the answer to the first one is C, because its the first step towards getting a perpendicular line . The next step would be to bisect the angle formed by drawing a line between Q and the point between L and M.

Answer 36

(-5,1) --> (x,-y) --> (-5,-1) --> (-x,y) --> (5,-1) --> (-x,-y) --> (-5,1)
yes A

Answer 37

which question is C @welshfella ?

Answer 38

the first one

Answer 39

@welshfella wouldn't that be irrelevent to constrct an arc in the middle of that line?

Answer 40

this one? Which of these is likely to be his next step in constructing the perpendicular line?

Fix the compass at Q, and draw an arc below the line.
Fix the compass at L, and draw an arc above the line.
Without changing the width, and position of the compass, draw an arc between L and M.
Without changing the width of the compass, place the compass at M, and draw an arc.
??

Answer 41

yup
he says it's C

Answer 42

@welshfella do u think the others were right or wrong that me and Will decided on ?

Answer 43

this is what im thinking of