Question

Find the distance between point p and line ℓ. line ℓ contains points ( −2 , 1) and (4, 1). point p has coordinates (5, 7).

Option 1: 5 units
Option 2: 35√ or about 5.92 units
Option 3: 47√ or about 6.96 units
Option 4: 6 units

Answer 1

The distance between point p and line l is 6 units.

Step-by-step explanation:

To find the distance between a point and a line, we can use the formula of the perpendicular distance between a point and a line. In this case, the line l contains the points (-2, 1) and (4, 1), and the point p has coordinates (5, 7). The formula is:

d = |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. In this case:

A = 1 - 1 = 0

B = 4 - (-2) = 6

C = -2 - 4 = -6

x = 5

y = 7

Plugging these values into the formula:

d = |0*5 + 6*7 + (-6)| / sqrt(0^2 + 6^2)

d = |0 + 42 - 6| / sqrt(0 + 36)

d = |36| / sqrt(36)

d = 36 / 6

d = 6

Therefore, the distance between point p and line l is 6 units. Option 4 is correct.