Question

In Exercises 21-24, find the distance from point A to the

given line. (See Example 5.)
21. A(-1,7), y = 3x
22. A(-9, -3), y = x - 6
23. A(15, -21), 5x + 2y = 4
24. Al -5,5), -x + 2y = 14

Answer 1

To find the distance from a point to a given line, we can use the formula for the distance between a point and a line. Let's apply this formula to each of the given lines.

Step-by-step explanation:

To find the distance from a point to a given line, we can use the formula for the distance between a point and a line. The formula is:

distance = |Ax + By + C| / sqrt(A^2 + B^2)

where A, B, and C are the coefficients of the line equation, and (x, y) are the coordinates of the point. Let's apply this formula to each of the given lines:

21. A(-1,7), y = 3x:

A = 3, B = -1, C = 0

distance = |3(-1) + (-1)(7) + 0| / sqrt(3^2 + (-1)^2) = 2 / sqrt(10)

22. A(-9, -3), y = x - 6:

A = 1, B = -1, C = 6

distance = |(-9) + (-1)(-3) + 6| / sqrt(1^2 + (-1)^2) = 4 / sqrt(2)

23. A(15, -21), 5x + 2y = 4:

A = 5, B = 2, C = -4

distance = |5(15) + 2(-21) - 4| / sqrt(5^2 + 2^2) = 66 / sqrt(29)

24. A(-5,5), -x + 2y = 14:

A = -1, B = 2, C = -14

distance = |-(-5) + 2(5) - 14| / sqrt((-1)^2 + 2^2) = 8 / sqrt(5)