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juin [17]
3 years ago
12

How to do this help please

Mathematics
1 answer:
andre [41]3 years ago
6 0

Answer:

y = - \frac{8}{15} x + \frac{289}{15}

Step-by-step explanation:

The angle between the tangent and the radius at point P is 90°

Calculate the slope of the radius m using the slope formula

m = (y₂ - y₁ ) / (x₂ - x₂ - x₁ )

with (x₁, y₁ ) = (0, 0) and (x₂, y₂ ) = (8, 15)

m = \frac{15-0}{8-0} = \frac{15}{8}

Given a line with slope m then the slope of a line perpendicular to it is

m_{perpendicular} = - \frac{1}{m} = - \frac{1}{\frac{15}{8} } = - \frac{8}{15}, thus

y = - \frac{8}{15} x + b ← is the partial equation

To find b substitute (8, 15) into the partial equation

15 = - \frac{64}{15} + b ⇒ b = 15 + \frac{64}{15} = \frac{289}{15}

y = - \frac{8}{15}  x + \frac{289}{15} ← equation of tangent

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Step-by-step explanation:

1) This is a vocabulary question. The <em>orthocenter</em> is the point where the altitudes intersect. Of course, each altitude is a segment from a vertex that is perpendicular to the opposite side of the triangle.

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