The proposed location for a new oil platform is represented in a coordinate plane by a rectangle with vertices A (1, -3), B (1, 4), C (4, 4), and D (4, -3). An inspector recommends moving the oil platform 4 units right and 2 units down. Find the coordinates of the image. Then draw the original figure and the image in the coordinate plane.
The proposed location for a new oil platform is represented in a coordinate plane by a rectangle with vertices A (1, -3), B (1, 4), C (4, 4), and D (4, -3). An inspector recommends moving the oil platform 4 units right and 2 units down. Find the coordinates of the image. Then draw the original figure and the image in the coordinate plane.
Step 1: We know that to translate a figure ‘a’ units horizontally and ‘b’ units vertically in the coordinate plane, ‘a’ is to be added to the
x-coordinate and ‘b’ is to be added to the y-coordinates of the vertices. Then new coordinates become:-
A (x,y) = A'(x+a, y+b)
The value ‘a’ and ‘b’ will be positive if the shift is Right and Vertical up respectively and the value of ‘a’ and ‘b’ will be negative if the shift is left and vertical down respectively.
Now we have given:
A(1,-3), B(1,4), C(4,4), D(4,-3) and a = 4, b = -2
A'(1+a, -3+b) = A'(1+4, -3-2) = A'(5,-5)
B'(1+a, 4+b) = B'(1+4, 4-2) = B'(5,2)
C'(4+a, 4+b) = C'(4+4, 4-2) = C'(8,2)
D'(4+a, -3+b) = D'(4+4, -3-2) = D'(8,-5)
Hence the coordinate of image are A'(5,-5), B'(5,2), C'(8,2), D'(8,-5)
Final Answer: Hence the coordinate of image are A'(5,-5), B'(5,2), C'(8,2), D'(8,-5)
Step 1: We know that to translate a figure ‘a’ units horizontally and ‘b’ units vertically in the coordinate plane, ‘a’ is to be added to the
x-coordinate and ‘b’ is to be added to the y-coordinates of the vertices. Then new coordinates become:-
A (x,y) = A'(x+a, y+b)
The value ‘a’ and ‘b’ will be positive if the shift is Right and Vertical up respectively and the value of ‘a’ and ‘b’ will be negative if the shift is left and vertical down respectively.
Now we have given:
A(1,-3), B(1,4), C(4,4), D(4,-3) and a = 4, b = -2
A'(1+a, -3+b) = A'(1+4, -3-2) = A'(5,-5)
B'(1+a, 4+b) = B'(1+4, 4-2) = B'(5,2)
C'(4+a, 4+b) = C'(4+4, 4-2) = C'(8,2)
D'(4+a, -3+b) = D'(4+4, -3-2) = D'(8,-5)
Hence the coordinate of image are A'(5,-5), B'(5,2), C'(8,2), D'(8,-5)
Final Answer: Hence the coordinate of image are A'(5,-5), B'(5,2), C'(8,2), D'(8,-5)
