Fractions and Decimals

Discrete Mathematics

Differential Equations

Solved on Nov 17, 2023

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

STEP 1

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

STEP 2

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

STEP 3

Let's analyze each option one by one.
1.3 units right;5 units down This would be represented as $(x, y) \rightarrow(x+3, y-5)$ or $_{<3,-5>}$ . 2.5 units left;3 units up This would be represented as $(x, y) \rightarrow(x-5, y+3)$ or $_{<-5,3>}$ .
3. $_{<-5,3>}$ This represents a translation of5 units to the left and3 units up. . $_{<5,-3>}$ This represents a translation of5 units to the right and3 units down.
5. $(x, y) \rightarrow(x-5, y+3)$ This represents a translation of5 units to the left and3 units up.
6. $(x, y) \rightarrow(x+5, y-3)$ 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 $\triangle R$ to \Delta R^{\prime}^{\prime}^{\prime} are1. units left;3 units up2. $_{<-,3>}$
3. $(x, y) \rightarrow(x-, y+3)$

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