Question

The length of segment AB with A(-1,5) and B(7,2) is about ___________ centimeter. a) √73 units

b) √56 units
c) √66 units
d) √89 units

Answer 1

The length of segment AB with A(-1,5) and B(7,2) is about √73 units. Option a is correct answer.

Step-by-step explanation:

The distance between two points in a coordinate plane can be calculated using the distance formula:

`\[d = √((x_2 - x_1)^2 + (y_2 - y_1)^2)\]`

For the given points A(-1,5) and B(7,2), the distance AB is:

`\[d = √((7 - (-1))^2 + (2 - 5)^2)\]`

`\[d = √(8^2 + (-3)^2)\]`

`\[d = √(64 + 9)\]`

`\[d = √(73)\]`

Therefore, the length of segment AB is √73 units.

In the coordinate plane, the distance formula essentially calculates the length of the hypotenuse of a right-angled triangle formed by the given points. The horizontal and vertical differences between the points serve as the triangle's legs. Applying the Pythagorean theorem (a² + b² = c²), where 'a' and 'b' are the differences in the x and y coordinates, respectively, and 'c' is the distance, we arrive at the square root of the sum of the squared differences, giving us the length of the segment.

In this case, the calculation yields √73, indicating that the length of segment AB is approximately equal to the square root of 73 units. Therefore, the correct answer is option a, √73 units.