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3 years ago

Find the value of y.

Mathematics

1 answer:

snow_tiger [21]3 years ago

4 0

Answer:

y = √55

Step-by-step explanation:

All the triangles are similar, so the ratio of short side to hypotenuse is the same for all:

5/y = y/(5+6)

y^2 = 55

y = √55

_____

Comment on the geometry

There are three "geometric mean" relationships that apply to this geometry.

the altitude BD is the geometric mean of BC and BA (√30)
the long side of the large triangle is the geometric mean of the longer segment of the hypotenuse and the whole hypotenuse (x = √66)
the short side of the large triangle is the geometric mean of the shorter segment of the hypotenuse and the whole hypotenuse (y = √55)

If you were aware of the last of these relationships, you could write down the answer without any "work."

y = √(5(5 +6)) = √55

The geometric mean is the n-th root of the product of n numbers. When there are 2 numbers, it is the square root of their product.

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Step-by-step explanation:

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Let C(10, -5) be (x₁, y₁) and Point D be (x₂, y₂). The midpoint M is (4, 0). Hence:

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Solve for each:

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And:

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