Question

Points A and B have the coordinates shown below.

Estimate the length of AB to the nearest tenth of a unit.
A= (-4,7)
B= (-12, -10)
AB = units

Answer 1

AB = 18.8 units

Explanation:

If there are two points (x1,y1) and (x2,y2) on the coordinate plane.

distance between those two points =
`\sqrt{(x1-x2)^(2) + (y1-y2)^(2) }`

given points are

A= (-4,7)

B= (-12, -10)

`AB = \sqrt{(-4 -(-12))^(2) + (7-(-10))^(2) }\\AB = \sqrt{(-4 +12)^(2) + (7+10)^(2) }\\AB = \sqrt{(8)^(2) + (17)^(2) }\\AB = √(64 + 289 )\\AB = √(353 )\\AB = 18.79`

Thus, length of AB is 18.79 units

since, value of hudredth of unit is 9 which is greater than 9 then rounding the value to nearest tenth of unit we increase the value at tenth of unit place by that is 7 becomes 8

length of AB to the nearest tenth of a unit is 18.9 units

Answer 2

Distance AB is 18.79 units

Explanation:

Given two points with coordinates as:

A= (-4,7)

B= (-12, -10)

To find:

Distance AB = ?

Solution:

To find the distance between two points with given coordinates, we can use Distance formula.

Distance formula is given as:

`D = √((x_2-x_1)^2+(y_2-y_1)^2)`

where
`(x_1, y_1)` and
`(x_2, y_2)` are the two coordinates whose distance is to be find out.

`x_1 = -4\\y_1 = 7\\x_2 = -12\\y_2 = -10`

`AB = √((-12-(-4))^2+(-10-7)^2)\\\Rightarrow AB = √((-8)^2+(-17)^2)\\\Rightarrow AB = √(64+289)\\\Rightarrow AB = √(353)\\\Rightarrow \bold{AB = 18.79\ units }`

Distance AB is 18.79 units