Question

Polygons LMNO and L'M'N'O' are shown on the following coordinate grid:A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon LMNO is shown with vertex L on ordered pair 2, negative 2, vertex M on ordered pair 4, negative 2, vertex N on ordered pair 1, negative 3 and vertex O on ordered pair 5, negative 3. A polygon L prime, M prime N prime O prime with vertex L prime on ordered pair negative 3, negative 2, M prime on negative 3, negative 4, N prime on negative 4, negative 1 and O prime on negative 4, negative 5.

What

Answer 1

Polygons LMNO and L'M'N'O' are shown on the following coordinate grid:A coordinate grid is shown from positive 6 to negative 6 on the x-axis and from positive 6 to negative 6 on the y-axis. A polygon LMNO is shown with vertex L on ordered pair 2, negative 2, vertex M on ordered pair 4, negative 2, vertex N on ordered pair 1, negative 3 and vertex O on ordered pair 5, negative 3. A polygon L prime, M prime N prime O prime with vertex L prime on ordered pair negative 3, negative 2, M prime on negative 3, negative 4, N prime on negative 4, negative 1 and O prime on negative 4, negative 5.

What set of transformations is performed on LMNO to form L'M'N'O'?

A 90-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A 270-degree counterclockwise rotation about the origin followed by a translation 1 unit to the left
A translation 1 unit to the left followed by a 270-degree counterclockwise rotation about the origin
A translation 1 unit to the left followed by a 90-degree counterclockwise rotation about the origin

Answer 2

@mathmale

Answer 3

@mathmate

Answer 4

@misty1212

Answer 5

@nysha
If the problem is given in words without a figure, much of the challenge is on drawing the figure. In geometry problems, drawing the figure is half of the problem solved. In this case, since drawing is part of the question, drawing is like 3/4 of the problem solved.
So please go ahead and show us a figure drawn from the given ordered pairs (8 of them altogether). Either use squared/lined paper or use technology, such as desmos.com.
If the question comes with a figure, please post the figure so that we are on the same wavelength.

By the way, if you have done transformation rules, recall:
1. rotations are considered counterclockwise positive.
2.
rotations:
\(r_{90}:(x,y) \rightarrow (-y,x)\)
\(r_{180}= r_{90}^2:(x,y) \rightarrow (-x,-y) \)
\(r_{270}:(x,y)=r_{-90}:(x,y)=r_{90}^3:(x,y) \rightarrow (y,-x)\)
translations:
\(t(a,b):(x,y)\rightarrow (x+a, x+b)\)

You could actually solve the problem using these transformation rules without drawing a figure/diagram, but it is not recommended.

Answer 6

is it A

Answer 7

I do not work with letter answers, and I do not validate unsubstantiated answer choices because the latter encourages guessing.

Answer 8

ok but i don't get the question so

Answer 9

If you don't understand the question, then please start with understanding the question, and not attempting answers.
You can either watch this video:
https://www.khanacademy.org/math/geometry/hs-geo-transformations/hs-geo-transformations-intro/v/introduction-to-transformations
or read about transformations here:
https://www.mathsisfun.com/geometry/transformations.html

Answer 10

Ok, now you can start looking at the problem.
First question to ask:
Are the two shapes congruent?

Answer 11

yes

Answer 12

I don't work with given choices. In real life, mathematical problem do not come with choices.

Excellent, if the preimage (LMNO) and image (L'M'N'O') are congruent then we can rule out dilation.

Next question: Are orientations of sides preserved? Ex. does LM have the same orientation as L'M'?

Answer 13

yes

Answer 14

Do you know what orientation means?
For example, LM is pointing east (assuming UP is north), and L'M' is pointing south.
Are orientations preserved ?

Answer 15

no

Answer 16

Ok, if orientations are not preserved, then there is a rotation.

Do you know what is the meaning of counterclockwise and clockwise?

Answer 17

clockwise is turning to the right counterclowise is turning to the left

Answer 18

Right or left is very vague for rotations.
Have you seen a clock/watch with two needles?

Answer 19

*needles/hands

Answer 20

yes

Answer 21

it looks like this, right?
http://analog.onlineclock.net/simple/

Answer 22

The moving hand (seconds hand) is rotation clockwise.
In trigonometry and math, we consider (most of the time) counterclockwise is positive.
ok so far?

Answer 23

ya

Answer 24

Now, as we saw earlier, the segment LM (pointing east) has become L'M' (pointing south), would that be a rotation, and of how many degrees counterclockwise?

Answer 25

90

Answer 26

well, we're working with counterclockwise rotation direction, look at the diagram below:

Can you try again?