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Question
Point P is located at (7, 4) on a coordinate grid. Point P is translated 4 units to the left and 8 units down to create point P’.
Which measurement is closest to the distance between point P and point P’ in units?
Responses
A 8.98.9
B 4040
C 16.216.2
D 2.65
To find the distance between point P and point P', we can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
In this case, the coordinates for point P are (7, 4), and the coordinates for point P' after translation are (-3, -4).
Plugging these values into the distance formula, we get:
Distance = √((-3 - 7)^2 + (-4 - 4)^2)
= √((-10)^2 + (-8)^2)
= √(100 + 64)
= √164
Since none of the answer choices are √164, we can approximate the answer using a calculator:
√164 ≈ 12.806
The measurement closest to the distance between point P and point P' in units is 12.8.
Therefore, the correct answer is not provided in the answer choices.
To find the distance between point P and point P', we can use the distance formula. The distance formula is given by:
d = √((x2 - x1)^2 + (y2 - y1)^2)
Where (x1, y1) are the coordinates of point P and (x2, y2) are the coordinates of point P'.
In this case, (x1, y1) = (7, 4) and (x2, y2) = (7 - 4, 4 - 8) = (3, -4).
Plugging in these values into the distance formula:
d = √((3 - 7)^2 + (-4 - 4)^2)
= √((-4)^2 + (-8)^2)
= √(16 + 64)
= √80
≈ 8.94
Therefore, the measurement closest to the distance between point P and point P' in units is 8.9.
The correct answer is A) 8.9.
To find the distance between two points in a coordinate grid, you can use the distance formula, which is derived from the Pythagorean theorem.
The distance formula is: d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
In this case, let's assign coordinates to the two points:
Point P: (x1, y1) = (7, 4)
Point P': (x2, y2) = (7 - 4, 4 - 8) = (3, -4)
Substituting these values into the distance formula, we get:
d = sqrt((3 - 7)^2 + (-4 - 4)^2)
= sqrt((-4)^2 + (-8)^2)
= sqrt(16 + 64)
= sqrt(80)
= 8.94 (rounded to two decimal places)
So the nearest measurement to the distance between point P and point P' is approximately 8.94 units.
Among the given options, the closest measurement is A) 8.9.