Question

find the distance between each pair of points. if necessary, round to the nearest tenth. 22. j(2, -1), k(2, 5) 23. l(10, 14), m(-8, 14) 25. a(0, 3), b(0, 12) 26. c(12, 6), d(-8, 18) 28. q(12, -12), t(5, 12) 29. r(0, 5), s(12, 3)

Explanation:

Let's solve each problem one by one using the distance formula or by observing the coordinates (if they are vertical or horizontal lines).

Problem 22: \( J(2, -1) \), \( K(2, 5) \)

Step 1: Identify the type of line

Since the x - coordinates of \( J \) and \( K \) are the same (\( x = 2 \)), the line \( JK \) is a vertical line. The distance between two points on a vertical line \( (x,y_1) \) and \( (x,y_2) \) is given by \( |y_2 - y_1| \).

Step 2: Calculate the distance

Here, \( y_1=-1 \) and \( y_2 = 5 \). So the distance \( d=|5-(-1)|=|5 + 1|=|6| = 6 \).

Step 1: Identify the type of line

Since the y - coordinates of \( L \) and \( M \) are the same (\( y = 14 \)), the line \( LM \) is a horizontal line. The distance between two points on a horizontal line \( (x_1,y) \) and \( (x_2,y) \) is given by \( |x_2 - x_1| \).

Step 2: Calculate the distance

Here, \( x_1 = 10 \) and \( x_2=-8 \). So the distance \( d=|-8 - 10|=|-18| = 18 \).

Step 1: Identify the type of line

Since the x - coordinates of \( A \) and \( B \) are the same (\( x = 0 \)), the line \( AB \) is a vertical line. The distance between two points on a vertical line \( (x,y_1) \) and \( (x,y_2) \) is given by \( |y_2 - y_1| \).

Step 2: Calculate the distance

Here, \( y_1 = 3 \) and \( y_2=12 \). So the distance \( d=|12 - 3|=|9| = 9 \).

Answer:

The distance between \( J(2,-1) \) and \( K(2,5) \) is \( 6 \).

Problem 23: \( L(10, 14) \), \( M(-8, 14) \)