Question

Find the distance between the parallel lines. If necessary, round your answer to the nearest tenth. Coordinate plane shows two lines. Line y equals minus 3 times x plus 1 intersects at coordinates. Ordered pair 0 comma 1. Ordered pair 0.5 comma 0. Line y equals minus 3 times x plus 4 intersects at coordinates. Ordered pair 0 comma 4. Ordered pair 1.5 comma 0. Distance: units

Answer 1

Explanation:

To find the distance between two parallel lines, we can use the formula for the shortest distance between a point and a line.

Let's consider the two parallel lines given:

Line 1: y = -3x + 1

Line 2: y = -3x + 4

We are asked to find the distance between these lines. To do this, we need to find the shortest distance between any two points, one on each line.

From the given coordinates, we can identify two points on each line:

Line 1: Point A (0, 1), Point B (0.5, 0)

Line 2: Point C (0, 4), Point D (1.5, 0)

Now, let's find the distance between Line 1 and Line 2 using the formula for the shortest distance between a point and a line:

Distance = √[(y2 - y1)^2 + (x2 - x1)^2]

We can calculate the distance between Line 1 and Line 2 using the coordinates of Point A and Point D:

Distance = √[(0 - 1)^2 + (1.5 - 0)^2]

= √[1 + 2.25]

= √3.25

≈ 1.8 units

Therefore, the distance between the parallel lines is approximately 1.8 units when rounded to the nearest tenth.