If point S is located at (0, 0), point T is located at (0, 6), point U is located at (12, 0), and point V is located at (0, 10), what are the coordinates of point W that makes △STU ~ △SVW? A. (0,20)
B. (0,24)
C. (20.0)
D.(24,0)

The coordinates of the point W is ((5/9)·√65, -20/9)

Step-by-step explanation:

The given parameters are;

The location of point S = (0, 0)

The location of point T = (0, 6)

The location of point U = (12, 0)

The location of point V = (0, 10)

We have;

The length of segment ST = √((6 - 0)² + (0 - 0)²) = 6

The length of segment SU = √((12 - 0)² + (0 - 0)²) = 12

The length of segment TU = √((12 - 0)² + (10 - 0)²) = √(144 + 100) = 2·√(61)

The length of segment TU = 2·√(61)

The length of segment SV = √((10 - 0)² + (0 - 0)²) = 10

Therefore, we have for similar triangles;

SV/SU = SW/ST = UW/TU

Therefore;

SW = ST × SV/SU = 6 × 10/12 = 5

VW = TU × SV/SU = 2·√(61) × 10/12 = (5/3)·√(61)

Where the coordinates of the point W = (a, b), we have;

Length of VW = √((10 - b)² + (0 - a)²) = (5/3)·√(61)

(25/9)·(61) = (10 - b)² + a²

Length of SW = √((0 - b)² + (0 - a)²) = 5

25 = b² + a²

∴ a² = 25 - b²

Substituting the value of a² into the length of segment LW equation, gives;

(25/9)·(61) = (10 - b)² + a² = (10 - b)² + 25 - b²

(25/9)·(61) = (10 - b)² + 25 - b² = 100 - 20·b + b² + 25 - b²

(25/9)·(61) = 125 - 20·b

20·b = 125 - (25/9)·(61)

b = -20/9

a² = 25 - b² = 25 - (-20/9)² = 1625/81

a = √(1625/81) = (5/9)·√65

The coordinates of the point W = ((5/9)·√65, -20/9).

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step-by-step explanation:

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