Question

Triangle XYZ has vertices X(1,1), Y(1,4) and Z (2,1), as shown below. We perform transformations to the triangle, as follows. First slide triangle XYZ to the right 4 units. Then reflect the image in the x-axis. Then reflect the new image in the y-axis. Finally slide the newest image up 5 units. What are the coordinates of the vertices of the final triangle?

Answer 1

Good very good extremely good question

Answer 2

Solution :-

Step 1) :- Given that, Triangle XYZ has vertices X(1,1), Y(1,4) and Z (2,1). we have to slide the ∆ to the right side 4 units.

Result :-

• Assume X(1,1) = A(1,1), Y(1,4) = B(1,4) and Z(2,1) = C(2,1).
• 4 unit to the right = Slide to the right side by 4 units, which gives , A = 1 + 4 = 5, B = 1+4 = 5 and C = 2+4 = 6 x axis points and y -axis points will remain same.
• In fig.(1) we can see that ,Let new ∆ so formed is A'B'C'. New points are :-
• A' = (5, 1) (1+4 = 5)
• B' = (5,4) (1+4 = 5)
• C' = (6,1) (2+4 = 6)

Step 2) :- Reflect the image in the x - axis.

Result :- Fig.(2)

• Reflection is equal to opposite. (Positive sign of y - axis becomes negative.)
• Let A''B''C'' is new ∆ formed . After reflection new points are :-
• A'' = (5, -1)
• B'' = (5, -4)
• C'' = (6, -1)

Step 3) :- Reflect the new image in the y-axis.

Result :- Fig.(3)

• in y -axis reflection , Positive sign of x - axis becomes negative..
• Let A'''B'''C''' is new ∆ formed . After reflection new points are :-
• A''' = (-5, -1)
• B''' = (-5, -4)
• C''' = (-6, -1)

Step 4) :- Slide the image up 5 units.

Result :- Fig.(4)

• x - axis points remains same, y-axis points change by adding 5 units.
• Let A''''B''''C'''' is new ∆ formed . After 5 units up new points are :-
• A'''' = (-5, 4) { - 1 + 5 = 4. }
• B'''' = (-5, 1) { - 4 + 5 = 1. }
• C'''' = (-6, 4) { - 1 + 5 = 4. }

Hence,

The coordinates of the vertices of the Final Triangle are :-

• A'''' = (-5, 4) .
• B'''' = (-5, 1) .
• C'''' = (-6, 4) .