The rule as a mapping for the translation of a rectangle is (x, y) → (x – 2, y + 7). Which describes this translation?
2 answers:
Answer:
This indicates a movement of 2 units to the left and 7 units upward.
Detailed explanation:
The fundamental principle of translation is
.... (1)
When a>0, the figure shifts a units to the right, while if a<0, it moves a units to the left.
For b>0, the figure goes b units up, and for b<0, it descends b units down
The specified rule of translation reads
.... (2)
By comparing (1) with (2), we deduce that
a = -2 < 0, indicating a movement of 2 units to the left.
b = 7 > 0, indicating a movement of 7 units upwards.
Thus, the stated rule reflects a translation of 2 units left and 7 units up.
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Now, we will substitute back
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.............Response
Answer:
The formula to determine the distance Jane's trainer bikes is .
Detailed explanation:
A diagram has been included for clarity.
Known values:
Distance biked to the south = 16 miles
Distance ran west = 12 miles
We need to determine the distance covered by Jane's trainer.
Solution:
Let the biking distance be represented by 'x'.
We will assume it forms a right-angled triangle.
According to the Pythagorean theorem, it states that;
"The square of the hypotenuse is equal to the sum of the squares of the other two sides."
When set in equation form, this gives us;
Thus, the equation representing the distance biked by Jane's trainer is .
Upon solving, we find;
Consequently, Jane's trainer covers a distance of 20 miles.
