Question

find the y coordinates of the points that are 5 units away from the point (3,3) that have an x coordinate of - 1. the y coordinates are (simplify your answer. use a comma to separate answers as needed )

Explanation:

Step1: Recall distance formula

The distance formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Here, $(x_1,y_1)=(3,3)$, $(x_2,y_2)=(-1,y)$, and $d = 5$.

Step2: Substitute values into formula

Substitute the values into the distance formula: $5=\sqrt{(-1 - 3)^2+(y - 3)^2}$. First, simplify $(-1 - 3)^2=(-4)^2 = 16$. So the equation becomes $5=\sqrt{16+(y - 3)^2}$.

Step3: Square both sides

Square both sides of the equation to get rid of the square - root: $25=16+(y - 3)^2$.

Step4: Isolate the squared term

Subtract 16 from both sides: $(y - 3)^2=25 - 16=9$.

Step5: Solve for y

Take the square root of both sides: $y - 3=\pm3$.

• Case 1: When $y - 3 = 3$, then $y=3 + 3=6$.
• Case 2: When $y - 3=-3$, then $y=-3 + 3=0$.

Answer:

0,6