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).
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)
5 answers
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)
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).
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
.(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.
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.
4 answers