Point E(−5, 3) and point D(−4, −3) are located on the grid. Which measurement is closest to the distance between point E and point D in units?
Responses
A 6.1 units6.1 units
B 5.3 units5.3 units
C 6.5 units6.5 units
D 6.7 units
To find the distance between two points on a grid, we can use the distance formula:
Distance = √( (x2 - x1)^2 + (y2 - y1)^2 )
For point E(-5,3) and point D(-4,-3), we can substitute the values into the formula:
Distance = √( ( -4 - (-5) )^2 + (-3 - 3)^2 )
= √( ( -4 + 5 )^2 + (-3 - 3)^2 )
= √( 1^2 + (-6)^2 )
= √( 1 + 36 )
= √37
Now, we need to find which measurement is closest to √37.
According to the given responses:
A) 6.1 units
B) 5.3 units
C) 6.5 units
D) 6.7 units
The closest measurement to √37 is B) 5.3 units.
To find the distance between two points on a grid, we can use the distance formula.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can calculate the distance between point E(-5, 3) and point D(-4, -3).
d = sqrt((-4 - (-5))^2 + (-3 - 3)^2)
= sqrt((1)^2 + (-6)^2)
= sqrt(1 + 36)
= sqrt(37)
Therefore, the distance between point E and point D is closest to 6.1 units.
The correct answer is A) 6.1 units.
To find the distance between two points on a grid, we can use the distance formula. The distance formula is:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2),
where (x1, y1) and (x2, y2) are the coordinates of the two points.
In this case, the coordinates of point E are (-5, 3), and the coordinates of point D are (-4, -3).
Plugging these values into the distance formula, we get:
d = sqrt((-4 - (-5))^2 + (-3 - 3)^2)
= sqrt((1)^2 + (-6)^2)
= sqrt(1 + 36)
= sqrt(37).
To find which measurement is closest to the distance between E and D, we need to compare the value of sqrt(37) to the given options.
Checking the options, we find that:
A) 6.1 units - Not a close approximation.
B) 5.3 units - Not a close approximation.
C) 6.5 units - Not a close approximation.
D) 6.7 units - This option is the closest approximation to sqrt(37).
Therefore, the answer is D) 6.7 units.