Question

Radius of circle O has a slope of 2.5. What is the slope of the line tangent to circle O at point A?

A.
0.8
B.
2.5
C.
-0.4
D.
-5

Answer 1

- 0.4

Explanation:

The radius of a circle and a tangent to the circle are perpendicular to each other at the point of contact.

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

`m_(perpendicular)` = -
`(1)/(m)` = -
`(1)/(2.5)` = - 0.4

Answer 2

-0.4

Explanation:

Given

Let r = radius

r = -2.5

The relationship between the slope of the tangent of the line and the radius is as follows;

Let ∆s represent slope

Mathematically, ∆s = -1/r

Substitute 2.5 for r

∆s = -1/2.5

∆s = -0.4

Hence, given that the radius of circle is 2.5, the slope of the line tangent to is -0.4