What is the midpoint between point A and B if point A is at (7, −4)
and point B is at (−9, 5). (1 point)
Responses
(−1,1/2)
(8, 1/2)
(8, 9/2)
(−1, 92)
To find the midpoint between two points, we can use the midpoint formula:
Midpoint = ( (x1 + x2) / 2, (y1 + y2) / 2 )
Given the points A (7, -4) and B (-9, 5), we can substitute the coordinates into the formula:
Midpoint = ( (7 + (-9)) / 2, (-4 + 5) / 2 )
Simplifying this, we get:
Midpoint = ( (-2) / 2, 1 / 2 )
which further simplifies to:
Midpoint = ( -1, 1/2 )
Therefore, the midpoint between points A and B is (-1, 1/2), so the correct answer is (−1, 1/2).
If the midpoint of line segment XY is at (2, 8) and point X is at (10, 4), what is the ordered pair of point Y? (1 point)
Responses
(4, −2)
(6, 6)
(5, 2)
(−6, 12)
To find the ordered pair of point Y, we can use the midpoint formula in reverse:
Midpoint = ( (x1 + x2) / 2, (y1 + y2) / 2 )
Given the midpoint (2, 8) and point X (10, 4), we can substitute the coordinates into the formula and solve for Y:
(2, 8) = ( (10 + x2) / 2, (4 + y2) / 2 )
Simplifying, we get:
2 = (10 + x2) / 2 -> multiplying both sides by 2 to eliminate the fraction: 4 = 10 + x2 -> x2 = -6
8 = (4 + y2) / 2 -> multiplying both sides by 2 to eliminate the fraction: 16 = 4 + y2 -> y2 = 12
Therefore, the ordered pair of point Y is (-6, 12). So, the correct answer is (−6, 12).
What is the distance between points J and K if J is at (−3, 2) and K is at (1, −6)
.(1 point)
Responses
4√5
2√5
4√3
2√3
2 square root of 3
To find the distance between two points, we can use the distance formula:
Distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Given that point J is (-3, 2) and point K is (1, -6), we can substitute the coordinates into the formula:
Distance = sqrt((1 - (-3))^2 + (-6 - 2)^2)
Simplifying this, we get:
Distance = sqrt((4)^2 + (-8)^2)
Distance = sqrt(16 + 64)
Distance = sqrt(80)
The square root of 80 can be simplified as sqrt(16*5), which further simplifies to 4 * sqrt(5).
Therefore, the distance between points J and K is 4√5. So, the correct answer is 4√5.
To find the midpoint between two points, you can use the midpoint formula. The formula is:
Midpoint = ((x1 + x2)/2, (y1 + y2)/2)
Here, point A has coordinates (7, -4) and point B has coordinates (-9, 5).
Using the midpoint formula, we can calculate the midpoint as follows:
Midpoint = ((7 + (-9))/2, (-4 + 5)/2)
Midpoint = (-2/2, 1/2)
Midpoint = (-1, 1/2)
Therefore, the midpoint between point A and B is (-1, 1/2).
So the correct answer is: (−1,1/2)
To find the midpoint between two points, we can use the midpoint formula. The midpoint formula states that the coordinates of the midpoint between two points (x1, y1) and (x2, y2) are given by:
midpoint = ((x1 + x2)/2, (y1 + y2)/2)
In this case, point A is located at (7, -4) and point B is located at (-9, 5).
Using the midpoint formula, we can calculate the midpoint as follows:
midpoint = ((7 + -9)/2, (-4 + 5)/2)
= (-2/2, 1/2)
= (-1, 1/2)
Therefore, the correct answer is (-1, 1/2), option A.