Mathematics, 01.10.2019 07:30 cofran

What series of transformations to quadrilateral abcd map the quadrilateral onto quadrilateral efgh to prove that abcd≅efgh ?

a reflection across x-axis, and then a translation 4 units left

a reflection across x-axis, and then a translation 4 units right

a reflection across y-axis, and then a translation 4 units right

a reflection across y-axis, and then a translation 4 units left

What series of transformations to quadrilateral abcd map the quadrilateral onto quadrilateral efgh

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Answer from: tbixler2021

B: a reflection across the x-axis followed by a translation 4 units right.

Comparing the points to their mapped images compares A to E, B to F, C to G, and D to H. In each point, the y-coordinate switches signs and the x-coordinate is subtracted by 4.

Reflections across the x-axis will switch the sign of the y-coordinate, and reflections across the y-axis will switch the sign of the x-coordinate. Since the y-coordinates are the ones whose sign changed, the points must have been reflected across the x-axis.

Translations to the left will cause the x-coordinate to increase, and translations to the right will case the x-coordinate to decrease. Since the x-coordinate of every point was subtracted, this means that the translation must have been to the right.

Answer from: Quest

"it's not the heat, it's the humidity". that's a partly valid phrase you may have heard in the summer, but it's actually both. the heat index, also known as the apparent temperature, is what the temperature feels like to the human body when relative humidity is combined with the air temperature. this has important considerations for the human body's comfort. when the body gets too hot, it begins to perspire or sweat to cool itself off. if the perspiration is not able to evaporate, the body cannot regulate its temperature. evaporation is a cooling process. when perspiration is evaporated off the body, it effectively reduces the body's temperature. when the atmospheric moisture content (i.e. relative humidity) is high, the rate of perspiration from the body decreases. in other words, the human body feels warmer in humid conditions. the opposite is true when the relative humidity decreases because the rate of perspiration increases. the body actually feels cooler in arid conditions. there is direct relationship between the air temperature and relative humidity and the heat index, meaning as the air temperature and relative humidity increase (decrease), the heat index increases (decreases).

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