Question

monday

1. how far is it from a to b?

a = 10 b = 10
a = 0 b = -10
a = -2 b = 3
a = -5 b = 1

1. find the radius.

Explanation:

Step1: Calculate distance between two points on number line

The distance formula between two points \(A\) and \(B\) on a number line is \(d = |A - B|\).

• When \(A = 10\) and \(B = 16\), \(d=|10 - 16|=|-6| = 6\).
• When \(A = 0\) and \(B=-10\), \(d = |0-(-10)|=|10| = 10\).
• When \(A=-2\) and \(B = 3\), \(d=|-2 - 3|=|-5| = 5\).
• When \(A=-5\) and \(B = 1\), \(d=|-5 - 1|=|-6| = 6\).

Step2: Find radius of the circle

The radius \(r\) of a circle with center \((0,0)\) and a point \((5,0)\) on the circle. Using the distance formula \(d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}\), here \(x_1 = 0,y_1 = 0,x_2 = 5,y_2 = 0\). So \(r=\sqrt{(5 - 0)^2+(0 - 0)^2}=\sqrt{25}=5\).

Answer:

1. The distances are \(6\), \(10\), \(5\), \(6\) respectively.
2. The radius is \(5\).