Question

What is the distance between point A (10, 14) and point B (16, 19) on the coordinate plane?

a) 5 units
b) 6 units
c) 7 units
d) 8 units

Answer 1

The distance between point A (10, 14) and point B (16, 19) on the coordinate plane is approximately 7.81 units, with the closest given option being 7 units.

Step-by-step explanation:

The distance between two points on a coordinate plane can be found using the distance formula, which is derived from the Pythagorean theorem. The distance formula is
`\(√((x_2-x_1)^2+(y_2-y_1)^2)\), where \((x_1, y_1)\) and \((x_2, y_2)\)` are the coordinates of the two points.

In the case of point
`A \((10, 14)\) and point B \((16, 19)\)`, we calculate the distance as follows:

• First, subtract the x-coordinates:
  `\(16 - 10 = 6\).`
• Next, subtract the y-coordinates:
  `\(19 - 14 = 5\).`
• Square both differences:
  `\(6^2 = 36\) and \(5^2 = 25\).`
• Add the squared differences:
  `\(36 + 25 = 61\).`
• Finally, take the square root of the sum:
  `\(√(61)\), which is approximately 7.81 units.`

Therefore, the distance between point A and point B is approximately 7.81 units. This is not an exact match to any of the options provided, but the closest option is:

c) 7 units