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Maths-

General

Easy

Question

In the xy-plane, the graph of y = (x - 6)² + 3 is the image of the graph of y = (x + 5)² + 3 after a translation of how many units to the right?

11

The correct answer is: 11

HINT: Find the coordinates from the given equations and then compare.
Complete step by step solution:
Let y = (x - 6)² + 3…(i) and y = (x + 5)² + 3…(ii)
From (i), we get (x₁, y₁) = (6, 3) and from (ii) we get (x₂, y₂) = (-5, 3)
We know that the distance formula, $straight d space equals space square root of open parentheses straight x subscript 2 space minus space straight x subscript 1 close parentheses squared space plus space open parentheses straight y subscript 2 space minus space straight y subscript 1 close parentheses squared end root$
On substituting the values, we get $straight d space equals space square root of left parenthesis negative 5 space minus space 6 right parenthesis squared space plus space left parenthesis 3 space minus space 3 right parenthesis squared space end root equals space square root of 121 space end root equals space 11$
So there is a translation of 11 units to the right.

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