Hector drew
Δ
N
O
P
∆
N
O
P
with the coordinates
(
4
,
2
)
4
,
2
,
(
5
,
3
)
5
,
3
, and
(
6
,
2
)
6
,
2
. Then, he drew an image of this triangle with coordinates
(
−
4
,
2
)
-
4
,
2
,
(
−
5
,
3
)
-
5
,
3
, and
(
−
6
,
2
)
-
6
,
2
. What is the line of reflection for this image?
Sorry, but that doesn't make any sense!
Please make sure you read your assignment!
at least retype it without all the line feeds!
Baby needs to use the space bar instead of the Enter key in most places -- like this --
Hector drew ΔNOP ...
To find the line of reflection for the given image, we need to identify the reflection of each point across the line of reflection.
Let's label the original triangle points as A (4, 2), B (5, 3), and C (6, 2). The corresponding image points are A' (-4, 2), B' (-5, 3), and C' (-6, 2).
To find the line of reflection, we can make use of the midpoint formula, which states that the midpoint between a point and its reflection is on the line of reflection.
Let's find the midpoint of two corresponding points:
Midpoint of AA': (4 + (-4))/2 = 0/2 = 0
Midpoint of BB': (5 + (-5))/2 = 0/2 = 0
Midpoint of CC': (6 + (-6))/2 = 0/2 = 0
The midpoints of AA', BB', and CC' all have an x-coordinate of 0. Therefore, the line of reflection is the vertical line passing through the point (0, 0).
Now, let's graph the original triangle ABC and its reflection:
Triangle ABC: Points A(4, 2), B(5, 3), C(6, 2)
Triangle A'B'C': Points A'(-4, 2), B'(-5, 3), C'(-6, 2)
The line of reflection is the vertical line passing through (0, 0).