Answer to Question #145548 in Geometry for Mason

Question

an architect is designing a garden for a client on the planning sheet. The client requests the relocation of a water fountain by the rule (x,y) to (x+7,y-8). later, the client decides that they would prefer the water fountains location moved from this new position to units left and three units up. Find the composition as a single transformation

Answer 1

$O(x, y)\to O'(x+7, y-8)$

$O'(x+7, y-8)\to O''(x+7-2, y-8+3)$ or $O''(x+5, y-5)$

Solution: $O''(x+5, y-5)$.