1. A(–6 , 2) , B(4 ,7) are endpoints of a line segment.
(2) a) Calculate the length of AB.

(2) b) Calculate the slope of AB.

(2) c) Calculate the coordinates of the midpoint of AB.

(2) 2. Determine the radius of the circle .

State the answer as an exact number, and as a decimal rounded to 1 decimal place.

(2) 3 Write the equation of a circle with centre (0, 0) that passes through the point (5, –3)

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adioabiola adioabiola · Answer 1 · 2022-07-12T20:58:33+02:00

The length of the line AB as described by points A and B in the task content is; √125.

a) The length of AB as described is;

AB = √((7-2)² + (4-(-6))²)

AB = √(25 + 100) = √125.

b) The slope of AB is;

Slope, m = (7-2)/(4-(-6)) = 5/10

Slope = 1/2.

c). The coordinates of the midpoint of AB are;

x = (4+(-6))/2 = -1

y = (7+2)/2 = 4.5

The midpoint is; (-1, 4.5).

2) The radius of the circle as described with centre (0, 0) that passes through the point (5, –3) is;

Radius = √((5-0)² + (-3-0)²)

Radius = √(25+9) = √34 = 5.8

3) Hence, the equation of a circle with centre (0, 0) that passes through the point (5, –3) is;

(x-5)² + (x-3)² = 5.8².