Which expression gives the distance between the points (−7,4) and (2,4)
?
A.
|4|+|4|
B.
|−7+2|
C.
|4−4|
D.
|−7|+|2|
B.
To find the distance between two points, we use the distance formula:
d = sqrt((x2-x1)^2 + (y2-y1)^2)
In this case,
x1 = -7
y1 = 4
x2 = 2
y2 = 4
Plugging in these values, we get:
d = sqrt((2-(-7))^2 + (4-4)^2)
Simplifying, we get:
d = sqrt(81)
d = 9
Therefore, the distance between the points (-7,4) and (2,4) is 9.
Note: None of the answer choices are correct.
but, but, ...
the last choice of |−7|+|2| equals 9, the correct answer
although I find it strange that the answer is written in that expression
You are correct! I apologize for my mistake. The last choice |−7|+|2| actually does equal 9 and is the correct answer. The expression uses the absolute value function to find the distance between two points on a number line. As both −7 and 2 are the same distance from 0, subtracting their absolute values gives us the distance between the two points. Thank you for catching that error.
To find the distance between two points, in this case (−7,4) and (2,4), you can use the distance formula:
Distance = √((x2 - x1)^2 + (y2 - y1)^2)
Let's substitute the given values into the formula:
Distance = √((2 - (-7))^2 + (4 - 4)^2)
Simplifying this further:
Distance = √((2 + 7)^2 + (0)^2)
Distance = √(9^2 + 0)
Distance = √(81 + 0)
Distance = √81
Distance = 9
So, the distance between the points (−7,4) and (2,4) is 9.
Now, let's analyze the answer options given:
A. |4| + |4| = 8
B. |−7+2| = 5
C. |4−4| = |0| = 0
D. |−7| + |2| = 7 + 2 = 9
Based on the calculations above, we can see that option D, |−7| + |2|, gives the correct distance between the two points, which is 9. Therefore, the correct answer is option D.