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## Answers

Point 1 (x₁, y₁) = (6, 2)

Point 2 (x₂, y₂) = (2, -3)

Point on the y-axis (x₃, y₃) = (0, y₃)

Note: The value of x on any point on y-axis is 0 (zero). Therefore, x₃ = 0

Since we are looking for a point equidistant to (6,2) and (2, -3), the distant equation is:

(x₃ - x₁)² + (y₃ - y₁)² = (x₃ - x₂)² + (y₃ - y₂)²

Substitute the values given:

(0 - 6)² + (y₃ - 2)² = (0 - 2)² + (y₃ - -3)²

36 + (y₃)² -4y₃ + 4 = 4 + (y₃)² + 6y₃ + 9

(y₃)² - 4y₃ + 40 = (y₃)² + 6y₃ + 13

(y₃)² - (y₃)² - 4y₃ - 6y₃ = 13 - 40

-10y₃ = -27

-10y₃/-10 = -27/-10

**y₃ = 27/10**

Therefore, the point (x₃, y₃) equidistant to the given points (6, 2) and (2, -3) is (0, ).

**ANSWER:**(0, )