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)

5 answers

To find the midpoint between two points, we use the midpoint formula:

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

In this case, point A has coordinates (7, -4) and point B has coordinates (-9, 5).

Applying the formula:

Midpoint = ((7 - 9)/2, (-4 + 5)/2)
Midpoint = ((-2)/2, 1/2)
Midpoint = (-1, 1/2)

Therefore, the midpoint between point A and point B is (-1, 1/2).
What is the distance between points J and K if J is at (−3, 2)
and K is at (1, −6)
.(1 point)
Responses
To find the distance between two points, we use the distance formula:

Distance = √((x₂ - x₁)² + (y₂ - y₁)²)

In this case, point J has coordinates (-3, 2) and point K has coordinates (1, -6).

Applying the formula:

Distance = √((1 - (-3))² + (-6 - 2)²)
Distance = √((1 + 3)² + (-6 - 2)²)
Distance = √(4² + (-8)²)
Distance = √(16 + 64)
Distance = √80

Simplifying further:

Distance = √(16 * 5)
Distance = √16 * √5
Distance = 4√5

Therefore, the distance between point J and point K is 4√5.
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
To find the ordered pair of point Y, we can use the midpoint formula:

Midpoint = ((x₁ + x₂)/2, (y₁ + y₂)/2)

In this case, the midpoint is (2, 8) and point X has coordinates (10, 4).

Applying the formula:

(2, 8) = ((10 + x)/2, (4 + y)/2)

Simplifying further:

2 = (10 + x)/2 and 8 = (4 + y)/2

To isolate x, we can multiply both sides of the first equation by 2:

4 = 10 + x

Subtracting 10 from both sides:

-6 = x

To isolate y, we can multiply both sides of the second equation by 2:

16 = 4 + y

Subtracting 4 from both sides:

12 = y

Therefore, the ordered pair of point Y is (-6, 12).