Question

A marina is in the shape of a coordinate grid. Boat A is docked at (2.4, −3) and Boat B is docked at (−3.4, −3). The boats are ____ units apart. (3 points)

a
5.8
b
6.4
c
8.8
d
9.4

Answer 1

Answer:

option (a) 5.8 units

Step-by-step explanation:

$\underline{\underline{\bf \: coordinate \: geometry}}$

• Coordinates of a point are a pair of numbers which represent the position of a point in a two dimensional plane.
• Coordinate plane has two axes which are perpendicular to each other – x-axis and y-axis.
• Let the coordinates of a point be P(x, y)

x is the x-coordinate/abscissa

y is the y-coordinate/ordinate

• Quadrants :

First Quadrant : both x-coordinate and y-coordinate are positive.

Second Quadrant : x-coordinate is negative and y-coordinate is positive.

Third Quadrant : both x-coordinate and y-coordinate are negative.

Fourth Quadrant : x-coordinate is positive and y-coordinate is negative.

______________________________

The distance between two points is given by,

$= \sqrt{(x_2 - x_1)^{2} +(y_2 - y_1) {2} }$

Let A(2.4,-3) be (x1, y1)

B(-3.4,-3) be (x2, y2)

The distance between both the boats

$= \sqrt{ {( - 3.4 - 2.4)}^{2} + {( - 3 - ( - 3))}^{2} } \\ = \sqrt{ {( - 5.8)}^{2} + {( - 3 + 3)}^{2} } \\ = \sqrt{ {5.8}^{2} + {0}^{2} } \\ = \sqrt{ {5.8}^{2} } \\ = 5.8 \: units$

The boats are 5.8 units apart.