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Question Translate △RST\triangle RST to △R′S′T′\triangle R'S'T': 5 units left, 3 units up; (x,y)→(x+5,y−3)(x,y) \rightarrow (x+5, y-3)

Studdy Solution

STEP 1

Assumptions1. △R\triangle R and \Delta R^{\prime}^{\prime}^{\prime} are two triangles in a coordinate plane. . The translation of △R\triangle R to \Delta R^{\prime}^{\prime}^{\prime} is represented by a rule.
3. The rule for translation is represented in the form (x,y)→(x+a,y+b)(x, y) \rightarrow(x+a, y+b) where 'a' is the horizontal shift and 'b' is the vertical shift.
4. The notation <a,b>_{<a,b>} represents a translation of 'a' units horizontally and 'b' units vertically.

STEP 2

We need to determine the rule for the translation of △R\triangle R to \Delta R^{\prime}^{\prime}^{\prime}. This rule will be in the form of (x,y)→(x+a,y+b)(x, y) \rightarrow(x+a, y+b) or <a,b>_{<a,b>}.

STEP 3

Let's analyze each option one by one.
1.3 units right;5 units down This would be represented as (x,y)→(x+3,y−5)(x, y) \rightarrow(x+3, y-5) or <3,−5>_{<3,-5>}. 2.5 units left;3 units up This would be represented as (x,y)→(x−5,y+3)(x, y) \rightarrow(x-5, y+3) or <−5,3>_{<-5,3>}.
3. <−5,3>_{<-5,3>} This represents a translation of5 units to the left and3 units up. . <5,−3>_{<5,-3>} This represents a translation of5 units to the right and3 units down.
5. (x,y)→(x−5,y+3)(x, y) \rightarrow(x-5, y+3) This represents a translation of5 units to the left and3 units up.
6. (x,y)→(x+5,y−3)(x, y) \rightarrow(x+5, y-3) This represents a translation of5 units to the right and3 units down.

STEP 4

Based on the analysis in3, the rules for the translation of △R\triangle R to \Delta R^{\prime}^{\prime}^{\prime} are1. units left;3 units up2. <−,3>_{<-,3>}
3. (x,y)→(x−,y+3)(x, y) \rightarrow(x-, y+3)

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