Logan Chen
07/26/2023 · Elementary School

\( t \). a) Consider quadrilateral \( A B C D \). i) Which quadrilateral is a translation of \( A B C D \) ? ii) Complete the following statement: \( A(-10 ; 9) \rightarrow \) \( \qquad \) iii) Describe the translation in words. iv) State the rule for this translation in the form \( (x ; y) \rightarrow(\square ; \square) \). b) Consider the quadrilateral LMNO. i) Which quadrilateral is a reflection of LMNO? ii) Complete the following statement: \( M(-2 ;-8) \rightarrow \) \( \qquad \) iii) State the equation of the line in which LMNO has been reflected iv) State the rule for this reflection in the form \( (x ; y) \rightarrow(\square ; \square) \). c) Consider quadrilateral SRQP. i) Which quadrilateral is a translation of SRQP? ii) Complete the following statement: \( \mathrm{Q}(3 ; 1) \rightarrow \) \( \qquad \) iii) Describe the translation in words. iv) State the rule for this translation in the form \( (x ; y) \rightarrow(\square ; \square) \). d) Consider the quadrilateral HIJK. i) Which quadrilateral is a reflection of HIJK? ii) Complete the following statement: \( \mathrm{H}(10 ; 9) \rightarrow \) \( \qquad \) iii) State the equation of the line in which HIJK has been reflected. iv) State the rule for this reflection in the form \( (x ; y) \rightarrow(\square ; \square) \). e) Consider quadrilateral UVWT. i) Which quadrilateral is a reflection of UVWT in the line \( y=x \) ? ii) Complete the following statement: \( U(2 ;-8) \rightarrow \) \( \qquad \) iii) State the rule for this reflection in the form \( (x ; y) \rightarrow(\square ; \square) \)

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Calculate or simplify the expression \( \sin(45) \). Calculate the value by following steps: - step0: Calculate: \(\sin\left(45\right)\) Calculate or simplify the expression \( \cos(\pi/4) \). Calculate the value by following steps: - step0: Calculate: \(\cos\left(\frac{\pi }{4}\right)\) - step1: Calculate the trigonometric value: \(\frac{\sqrt{2}}{2}\) Calculate or simplify the expression \( \sin(45)/\cos(\pi/4) \). Calculate the value by following steps: - step0: Calculate: \(\frac{\sin\left(45\right)}{\cos\left(\frac{\pi }{4}\right)}\) - step1: Transform the expression: \(\frac{2\sin\left(45\right)}{\sqrt{2}}\) - step2: Multiply by the Conjugate: \(\frac{2\sin\left(45\right)\times \sqrt{2}}{\sqrt{2}\times \sqrt{2}}\) - step3: Multiply the numbers: \(\frac{2\sqrt{2}\times \sin\left(45\right)}{\sqrt{2}\times \sqrt{2}}\) - step4: Multiply the numbers: \(\frac{2\sqrt{2}\times \sin\left(45\right)}{2}\) - step5: Reduce the fraction: \(\sqrt{2}\times \sin\left(45\right)\) The value of \( \frac{\sin(45^{\circ})}{\cos(\frac{\pi}{4})} \) is \( \sqrt{2} \).

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\( \sqrt{2} \).
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