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3 years ago

Don't know how to express the value of X as any of those answer choices

Mathematics

1 answer:

Alekssandra [29.7K]3 years ago

3 0

9514 1404 393

Answer:

x = √(w(w+z))

Step-by-step explanation:

The idea with a right-triangle figure of this sort is that all of the triangles are similar. Here, x is the short side of ∆ABC, and the hypotenuse of ∆BDC. This suggests you want to write a similarity statement involving the short side and hypotenuse.

BC/AC = DC/BC . . . . . short side/hypotenuse

BC² = AC·DC . . . . . . cross multiply

x² = (w+z)w . . . . . . substitute letter values

Taking the square root and rearranging to the form of the applicable answer choice, this is ...

$\boxed{x=\sqrt{w(w+z)}}$

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3 years ago

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3 years ago

Read 2 more answers

The endpoints of are A(2, 3) and B(8, 1). The perpendicular bisector of is , and point C lies on . The length of is units. The c

Blababa [14]

Answer:

The Coordinates of Point C are C(5,2)

The slope of CD is 3

The possible coordinates of point D(a,b) are (6, 5) and (4, -1)

Step-by-step explanation:

According to the Question,

Given, The end points of AB are A(2,3) and B(8,1). The perpendicular Bisector of AB is CD, and point C lies on AB. The length of the CD is √10 units.

Now, Let The Coordinates of Point C are C( x , y ) .

Thus, C( x , y ) = ((8 +2) / 2 , ( 1 + 3 )/ 2 ) ⇒ (10/2 , 4/2) ⇒ (5 , 2)

The Coordinates of Point C are C( x , y ) ⇒C(5, 2).

And, The slope of AB = (1 - 3)/(8 - 2) ⇒ -2/6 ⇔ -1/3 .

Thus, The slope of CD is -1/(The slope of AB) = -1/(-1/3) ⇔ 3.

Let the coordinate of D be (a, b) then

⇒ √{ (b - 2)² +(a - 5)² } = √10

on squaring both sides we get,

⇒ a² - 10a + 25 + b² - 4b + 4 = 10

⇒ a² + b² - 10a - 4b = - 19 ⇔⇔ (Equation 1)

We Know, the slope of CD = 3

⇒Thus, (b - 2)/(a - 5) = 3

⇒ b - 2 = 3a - 15

⇒ b = 3a - 13 ⇔⇔ (Equation 2)

Putting value of Equation 2 into Equation 1, We get

⇒a² + (3a - 13)² - 10a - 4(3a - 13) = - 19

⇒a² + 9a² - 78a + 169 - 10a - 12a + 52 = - 19

⇒10a² - 100a + 240 = 0

⇒a² - 10a + 24 = 0

⇒(a - 4)(a - 6) = 0

⇒a = 4 or a = 6

Now,

When a = 4 , b = 3(4) - 13 ⇒ 12 - 13 ⇒ b = -1

When a = 6, b = 3(6) - 13 ⇒ 18 - 13 ⇒ b = 5

Therefore, the possible coordinates of point D(a,b) are (6, 5) and (4, -1).

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3 years ago