Question

find the y - coordinates of the points that are 5 units away from the point (-1,3) that have an x - coordinate of 3. 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 $d = \sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$. Let $(x_1,y_1)=(-1,3)$ and $(x_2,y_2)=(3,y)$. Given $d = 5$.

Step2: Substitute values into formula

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

Step3: Square both sides

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

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