Final answer:
To solve for yı in the equation d = √√(x₂-x₁)² + (y₂ − Y₁ )², we isolate yı by squaring both sides, isolating the term (y₂ − Y₁ )², and finally adding Y₁ to both sides.
Step-by-step explanation:
To solve the equation d = √√(x₂-x₁)² + (y₂ − Y₁ )² for yı, we need to isolate yı on one side of the equation. Let's start by squaring both sides of the equation to eliminate the square root: d² = (√(x₂-x₁)² + (y₂ − Y₁ )²)
Next, let's isolate (y₂ − Y₁ )² by subtracting (√(x₂-x₁)² from both sides:
(y₂ − Y₁ )² = d² - (√(x₂-x₁)²)
Finally, we take the square root of both sides to solve for (y₂ − Y₁ )²:
y₂ - Y₁ = ±√(d² - (√(x₂-x₁)²))
Thus, to solve for yı, we need to add Y₁ to both sides of the equation:
yı = ±√(d² - (√(x₂-x₁)²)) + Y₁
Learn more about Solving equations involving square roots