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Find all values of y such that the distance between (3,y) and
(−2,3) is 14.

1 Answer

2 votes

Final answer:

The values of y that satisfy the given condition are y = 3 and y = 7.

Step-by-step explanation:

To find the values of y such that the distance between (3,y) and (-2,3) is 14, we can use the distance formula. The distance formula is given by:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given coordinates and the distance:

14 = sqrt((-2 - 3)^2 + (3 - y)^2)

Simplifying the equation:

196 = 25 - 10y + y^2

Rearranging and solving for y:

y^2 - 10y + 171 = 0

Using the quadratic formula, we find two values of y: y = 3 or y = 7. Therefore, the values of y that satisfy the given condition are y = 3 and y = 7.

User Eraxillan
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