Question

If triangle HIJ is dilated about the center of the triangle to create triangle H′I′J′, dilated line A′B′ will

Answer 1

welcome to QC~

is there a list of choices or a diagram associated with this problem?

Answer 2

a.be perpendicular to AB
b. lie on the same line as AB
c.shift four units to the left
d.be parallel to AB

Answer 3

that it the list of the choices.

Answer 4

if you compare the line AB and the dilated red line A'B'

are they parallel? perpendicular? or something else?

Answer 5

try to look at my diagram

notice how the black line AB gets dilated to the red horizontal line

are the line AB and the red line parallel or perpendicular?

Answer 6

thanks

Answer 7

The coordinates of trapezoid ABCD are A(−4, 3), B(2, 3), C(4, −1) and D(−4, −1). A line segment runs through the trapezoid with endpoints Y(−4, 1) and Z(3, 1). If trapezoid ABCD is dilated by a scale factor of 3 creating the new trapezoid of A′B′C′D′, what can you say about the length of line segment Y′Z′?

Answer 8

"dilated by scale factor three" means that Y'Z' is three times as large as YZ

Answer 9

The length remains the same as the original line segment.
The length increases by a scale factor of 3.
The length decreases by a scale factor of 3.
The length is not able to be determined by the information given.

Answer 10

\(\color{#0cbb34}{\text{Originally Posted by}}\) @Mercury
"dilated by scale factor three" means that Y'Z' is three times as large as YZ
\(\color{#0cbb34}{\text{End of Quote}}\)

key phrase: "Three times as large"

Answer 11

Triangle HAM is translated using the rule (x,y)→(x+6, y) to create triangle H′A′M′. If a line segment is drawn from point H to point H′ and from point A to point A′, which statement would best describe the line segments drawn?

a. They share the same midpoints.
b. They are parallel and congruent.
c.They are diameters of concentric circles.
d.They are perpendicular to each other.

Answer 12

any attempts to sketch the problem?

Answer 13

so which statement out of the choices best describes these those blue lines?

Answer 14

those are not helping me

Answer 15

are those two lines parallel or perpendicular? are they the same length or different lengths?

Answer 16

they are the same length

Answer 17

good

but are they parallel or perpendicular?

Answer 18

they are parallel

Answer 19

good

so they are parallel and the same length

making which answer choice the correct one?

Answer 20

the correct answer is b. They are parallel and congruent.

Answer 21

well done

Answer 22

Triangle CAT is translated using the rule (x,y)→(x−3, y+4) to create triangle C′A′T′. If a line segment is drawn from point C to point C′ and from point A to point A′, which statement would best describe the line segments drawn?

Answer 23

same logic as last time

try sketching the two triangles, connecting the segments, and seeing if the two segments are perpendicular/parallel, etc.

you may use the previous problem as a reference.

let me know if you're getting stuck

Answer 24

thanks, I find it

Answer 25

Hexagon DEFGHI is translated on the coordinate plane below to create hexagon D′E′F′G′H′I′:



Which rule represents the translation of hexagon DEFGHI to hexagon D′E′F′G′H′I′?

a.(x, y)→(x + 4, x − 2)
b. (x, y)→(x − 7, y + 7)
c. (x, y)→(x + 2, x − 4)
d. (x, y)→(x + 7, y − 7)

Answer 26

so you want to pick two corresponding points and see the horizontal and vertical distance between them

so let's use D and D' as an example

what is the horizontal distance between D and D'?

Answer 27

I don't know

Answer 28

how many spaces did we go from D to D'?

Answer 29

one spaces Dto D

Answer 30

see how many little jumps we made from D to D'? try counting the jumps

Answer 31

7

Answer 32

awesome

so D --> D' we add 7 units to the x coordinate to get

x + 7

so the last choice is the only viable option

Answer 33

is going to be the y

Answer 34

notice how the only answer choice with x + 7 is the last choice d. (x, y)→(x + 7, y − 7)

Answer 35

thanks

Answer 36

The plate is rotated 90° about the origin in the counterclockwise direction. In the rotated trapezoid, what are the coordinates of the endpoints of the side congruent to side GH?

Answer 37

is there a diagram that goes with this?

Answer 38

first find the coordinates of G

then apply the rule (-y,x) to find the new coordinates of G

Answer 39

the coordinates of G are (-4,3), right? so x = -4 and y = 3

what do you get when you write the coordinates as (-y, x)?

Answer 40

I find what it is

Answer 41

The plate is rotated 90° about the origin in the counterclockwise direction. In the rotated trapezoid, what are the coordinates of the endpoints of the side congruent to side FG?

(a.7, −5) and (4, −3)
b. (5, 7) and (3, 4)
c. (−5, −7) and (−3, −4)
d. (−5, −7) and (−8, −4)