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3 years ago

Write a description of the rule (x, y) = (x - 4, y + 3).

Mathematics

1 answer:

storchak [24]3 years ago

4 0

9514 1404 393

Answer:

translate 4 left and 3 up

Step-by-step explanation:

The value added to the x-coordinate is the translation to the right. Here, it is -4, so the translation is 4 units left.

The value added to the y-coordinate is the translation up. Here, it is +3, so the translation is 3 units up.

The rule effects a translation 4 units left and 3 units up.

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In a right triangle ABC, CD is an altitude, such that AD=BC. Find AC, if AB=3 cm, and CD= 2 cm.

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Consider right triangle ΔABC with legs AC and BC and hypotenuse AB. Draw the altitude CD.

1. Theorem: The length of each leg of a right triangle is the geometric mean of the length of the hypotenuse and the length of the segment of the hypotenuse adjacent to that leg.

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$BC^2=BD\cdot AB.$

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$x^2=(3-x)\cdot 3,\\ \\x^2=9-3x,\\ \\x^2+3x-9=0,\\ \\D=3^2-4\cdot (-9)=9+36=45,\\ \\\sqrt{D}=\sqrt{45}=3\sqrt{5},\\ \\x_1=\dfrac{-3-3\sqrt{5} }{2}0.$

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