Question

which one is the correct distance formula?
o a) y = mx + b
o b) d = √((x₂ - y₂)² + (x₁ - y₁)²)
o c) d = √((x₂ - x₁)² + (y₁ - y₂)²)
o d) d = -b±√(b² - 4ac)/2a

Explanation:

Step1: Recall distance formula

The distance $d$ between two points $(x_1,y_1)$ and $(x_2,y_2)$ in a two - dimensional plane is given by the formula $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$.

Step2: Analyze each option

• Option A: $y = mx + b$ is the slope - intercept form of a line.
• Option B: The formula $d=\sqrt{(x_2 - y_2)^2+(x_1 - y_1)^2}$ is incorrect as it mixes the $x$ and $y$ coordinates in an improper way.
• Option C: $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$ is the correct distance formula.
• Option D: $d=\frac{-b\pm\sqrt{b^{2}-4ac}}{2a}$ is the quadratic formula for finding the roots of a quadratic equation $ax^{2}+bx + c=0$.

Answer:

C. $d=\sqrt{(x_2 - x_1)^2+(y_2 - y_1)^2}$