Question

A neighborhood planner uses a coordinate plane to design a new neighborhood. The coordinates $A(1,-1)$ A(1,−1)​ , $B\left(1,-2\right)$ B(1,−2)​ , and $C(2,-1)$ C(2,−1)​ represent House A, House B, and House C. The planner decides to place a playground centered at the origin, and moves the houses to make space. House A is now located at $A'(3,-4)$ A′(3,−4)​ . What are the new coordinates of House B and House C when each house is moved using the same translation?

Answer 1

Given :- The coordinates of A(1, -1) , B(1, -2) and C(2, - 1) represent House A, House B, and House C. The planner decides to place a playground centered at the origin, and moves the houses to make space. House A is now located at A'(3, -4) .

To Find :- What are the new coordinates of House B and House C when each house is moved using the same translation ?

Answer :-

we have,

→ Initial coordinates of hourse A = (1, -1)

→ final coordinates of hourse A = (3, -4)

conclusion :-

• x coordinates moves 2 points on right side of x axis .
• y coordinates moves 3 points down of y axis .

since, each house is moved using the same translation .

then, new coordinates of House B :-

• B(1, -2) = B'(1 + 2 , -2 - 3) = B'(3 , -5) .

and, new coordinates of House C :-

• C(2, -1) = B'(2 + 2 , -1 - 3) = B'(4 , -4) .

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