Questions: Complete the sentence below. The distance d between two points P1=(x1, y1) and P2=(x2, y2) is d=

Solution Steps

To find the distance \( d \) between two points \( P_1 = (x_1, y_1) \) and \( P_2 = (x_2, y_2) \), we use the distance formula derived from the Pythagorean theorem. The formula is:

\[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Given two points \( P_1 = (1, 2) \) and \( P_2 = (4, 6) \), we identify the coordinates:

• \( x_1 = 1 \)
• \( y_1 = 2 \)
• \( x_2 = 4 \)
• \( y_2 = 6 \)

The distance \( d \) between two points \( P_1 \) and \( P_2 \) is given by the formula: \[ d = \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2} \]

Substitute the coordinates into the distance formula: \[ d = \sqrt{(4 - 1)^2 + (6 - 2)^2} \]

Calculate the differences and squares: \[ d = \sqrt{3^2 + 4^2} \] \[ d = \sqrt{9 + 16} \] \[ d = \sqrt{25} \]

Final Answer