Question

A(-5,-4) ——> A’ is a glide reflection where the translation is (x,y)—->(x+6,y), and the line of reflection is y=3. What are the coordinates of A’?
A. (1,-4)
B. (-5,2)
C. (1,10)
D. (11,2)

Answer 1

Solution:

The Point in the coordinate plane is A(-5,-4).

Perpendicular or shortest Distance from line y=3 that is (-5,3) to point (-5,-4) is

$=\sqrt{(-5+5)^2+(3+4)^2}\\\\=7$

When it is reflected through the line, y=3, the coordinate of point A (-5,-4) changes to (-5,3+7)= B(-5,10).

Now, the Point B is translated by the rule , (x,y)—->(x+6,y),

So,the point B is translated to, (-5+6,10)=(1,10)

Option C: (1,10) is the glide reflection of point A(-5,-4).

Answer 2

The coordinates of A is $\boxed{\left( {1,10} \right)}.$

Further explanation:

Translation can be defined as to move the function to a certain displacement. If the points of a line or any objects are moved in the same direction it is a translation.

Explanation:

The translation mapping of a single translation can be expressed as follows,

$\left( {x,y} \right) \Rightarrow \left( {x + h,y + k} \right)$

Here, h represents the distance of translation in x-axis and k represents the distance of translation in y-axis.

The coordinates of A after reflection is $\boxed{\left( {- 5,- 4} \right)}.$

The translation rule is $\left( {x,y} \right) \to \left( {x + 6,y}\right)$

The coordinates after translation can be obtained as follows,

$A\left( { - 5,- 4} \right) \to \left( { - 5 + 6, - 4} \right) = \left( {1, - 4} \right)$

The reflection is along $y = 3$. Therefore, only y-coordinate will change and the x-coordinate remain the same.

-4 is 7 units below the reflection line $y = 3.$

Therefore, the coordinate of A after reflection can be obtained as follows,

$A\left( {1,3 + 7} \right) = \left( {1,10} \right)$

Hence, the coordinates of A is $\boxed{\left( {1,10} \right)}.$

Kindly refer to the image attached.

Learn more:

1. Learn more about inverse of the functionhttps://brainly.com/question/1632445.

2. Learn more about equation of circle brainly.com/question/1506955.

3. Learn more about range and domain of the function brainly.com/question/3412497

Answer details:

Grade: Middle School

Subject: Mathematics

Chapter: Triangles

Keywords: rotation, translation, triangle, rotation about point A, mapped, triangle pair, mapping, equal angles, sides, glide reflection, (x,y), (x+6,y), the line of reflection is y=1, coordinates of A.