Question

Find the distance between each pair of points:

A(–3, 8) and B(–1, 4)
M(4, –3) and N(–2, 1)

Answer 1

The distance between points A(–3, 8) and B(–1, 4) is approximately 4.47 units, and the distance between points M(4, –3) and N(–2, 1) is approximately 7.21 units. This is computed using the distance formula.

Step-by-step explanation:

The distance between two points on the Cartesian plane can be found using the distance formula: d = √((x2 - x1)2 + (y2 - y1)2).

For points A(–3, 8) and B(–1, 4), we apply the formula:

1. Calculate the difference in the x-coordinates: (–1) – (–3) = 2.
2. Calculate the difference in the y-coordinates: 4 – 8 = -4.
3. Apply the differences to the formula: √((2)2 + (-4)2) = √(4 + 16) = √20 ≅ 4.47 units.

For points M(4, –3) and N(–2, 1), we follow the same steps:

1. Calculate the difference in the x-coordinates: (–2) – 4 = -6.
2. Calculate the difference in the y-coordinates: 1 – (–3) = 4.
3. Apply the differences to the formula: √((-6)2 + (4)2) = √(36 + 16) = √52 ≅ 7.21 units.

Therefore, the distance between points A and B is approximately 4.47 units, and the distance between points M and N is approximately 7.21 units.