How many points are 3 units from the y-axis and 1 unit from (4,1)?

Intuitively we're being asked how many points on the radius 1 circle centered at (4,1) are three units from the y axis.  The answer is pretty obviously

One point

We'll work it out the usual way.

Let's give coordinates (x,y) to a point 3 units from the y axis and 1 unit from (4,1).

The x coordinate tells us how far we are from the y axis.  3 units from the y axis means

|x| = 3

x = ±3

One unit from (4,1) means

(x - 4)² + (y - 1)² = 1²

Let's try x=-3

(-7)² + (y - 1)² = 1

(y - 1)² = -48

No solution there

Let's try x=3

(3 - 4)² + (y - 1)² = 1

(-1)² + (y - 1)² = 1

(y - 1)² = 0

y - 1 = 0

y = 1

So (3,1) is the only point 3 units from the y axis and 1 unit from (4,1).

That verifies our answer above.

the letter

Step-by-step explanation: