Question

d√(x2 - x1)² + (y2 - y1)² find the distance between p and q

Explanation:

To find the distance between two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \), we use the distance formula:

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

However, we need the coordinates of points \( P \) and \( Q \) to compute the distance. Since the coordinates are not provided in the image, we can't calculate the numerical value. If we assume the coordinates of \( P \) are \( (x_1, y_1) \) and \( Q \) are \( (x_2, y_2) \), the distance formula is as above.

For example, if \( P(1, 2) \) and \( Q(4, 6) \):

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

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

Step 2: Substitute into the formula

\[
d = \sqrt{(4 - 1)^2 + (6 - 2)^2}
\]

Step 3: Simplify inside the square root

\[
d = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16}
\]

Step 4: Calculate the sum and take the square root

\[
d = \sqrt{25} = 5
\]

But without specific coordinates, we can only present the formula. If you provide the coordinates of \( P \) and \( Q \), we can compute the exact distance.

Answer:

To find the distance between two points \( P(x_1, y_1) \) and \( Q(x_2, y_2) \), we use the distance formula:

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

However, we need the coordinates of points \( P \) and \( Q \) to compute the distance. Since the coordinates are not provided in the image, we can't calculate the numerical value. If we assume the coordinates of \( P \) are \( (x_1, y_1) \) and \( Q \) are \( (x_2, y_2) \), the distance formula is as above.

For example, if \( P(1, 2) \) and \( Q(4, 6) \):

Step 1: Identify \( x_1, y_1, x_2, y_2 \)

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

Step 2: Substitute into the formula

\[
d = \sqrt{(4 - 1)^2 + (6 - 2)^2}
\]

Step 3: Simplify inside the square root

\[
d = \sqrt{(3)^2 + (4)^2} = \sqrt{9 + 16}
\]

Step 4: Calculate the sum and take the square root

\[
d = \sqrt{25} = 5
\]

But without specific coordinates, we can only present the formula. If you provide the coordinates of \( P \) and \( Q \), we can compute the exact distance.