Question

Please help ASAP 15 points

Answer 1

Answer:

$\boxed{\text{(a)}4\sqrt{5} \text{; (b)} -2}$

Step-by-step explanation:

(a) Radius of circle

The radius r of the circle is AB.

The coordinates of its ends are (5, 10) and (-3, 6).  

x = x₂ - x₁ = 5- (-3) = 5 + 3 = 8

y = y₂ - y₁ = 10 - 6 = 4

We can use the Pythagorean theorem to calculate its length.

r² = 8² + 4² = 64 + 16 = 80

r = √80 = 4√5

(b) Slope of line l

Slope of AB = 4/8 = ½

Line l⟂AB, so its slope is the negative reciprocal of the slope of AB .

m = -1/½ = -2

The radius of the circle is $\boxed{4\sqrt{5}}$ and the slope of line l is $\boxed{-2}$.