Derek's design is a kite which starts with coordinates: A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he translates it 5 units to the left and 3 units down and then reflects it across the y-axis, which of these would be correct? Select the two answers.

The answer is below

Step-by-step explanation:

Select the two answers

a.A would be at (-3,5)

b. B would be at (-1,5)

c.C would be at (-5,8)

d. It would end at the same spot if the original design was reflected across the x-axis,followed by a 180 degree rotation about the origin,followed by translation 1 unit to the left.

E.It would end at the same spot if the original design was reflected 180 degrees rotation about the origin,followed by a translation 3 unit up and translated 1 unit to the left

Select the two answers

a.A would be at (-3,5)

b. B would be at (-1,5)

c.C would be at (-5,8)

d. It would end at the same spot if the original design was reflected across the x-axis,followed by a 180 degree rotation about the origin,followed by translation 1 unit to the left.  

E.It would end at the same spot if the original design was reflected 180 degrees rotation about the origin,followed by a translation 3 unit up and translated 1 unit to the left

Solution:

Transformation is the movement of a point from its initial location to a new location. Types of transformation are reflection, rotation, translation and dilation.

If a point X(x, y) is translated b units up and a units right, the new point is X'(x + a, y + b). If a point X(x, y) is translated b units down and a units left, the new point is X'(x - a, y - b)

If X(x, y) is reflected across the y axis, the new point is X'(-x, y)

If X(x, y) is reflected across the x axis, the new point is X'(x, -y)

If X(x, y) is rotated 180 degrees, the new point is X'(-x, -y)

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he translates it 5 units to the left and 3 units down the new point is A'(-3, -3), B'(-1, -5), C'(-3, -8), D'(-5, -5). If it is then reflected across the y axis, the new point is A"(3, -3), B"(1, -5), C"(3, -8), D"(5, -5).

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he reflected across the x-axis the new point is A'(2,0), B'(4, 2), C'(2, 5), D'(0, 2). If it is then rotated 180 degrees, the new point is A"(-2, 0), B"(-4, -2), C"(-2, -5), D"(0, -2). If it is translated 1 unit left the point would be A"'(-3, 0), B"'(-5, -2), C"'(-3, -5), D"'(-1, -2)

If A(2, 0), B(4,-2), C(2,-5) and D(0,-2). If he rotated 180 degrees the new point is A'(-2, 0), B'(-4, 2), C'(-2, 5), D'(0, 2). If it is then translated it 3 units up and 1 units left, the new point is A"(-3, 3), B"(-5, 5), C"(-3, 8), D"(-1, 5).

an

y = 6x -3y -12

y +3y +12 = 6x

=> . x = { 2y / 3 +2 } this is equation of line in terms of x

=> . if line meets the x-axis the co-ordinates of meeting point would be ( x , 0 )

=> . x = 2 ( 0 ) / 3 + 2

=> . x = 2

so, the point is ( 2 , 0 )