Find the distance between each pair of points.

Question

Round your answer to the nearest tenth, if necessary.
(-2,-1), (6,8)

Find the midpoint of the line segment with the given endpoints.
(4, 5), (-10, -5)

Answer 1

To find the distance between two points (x1, y1) and (x2, y2), we can use the distance formula:

Distance = √[(x2 - x1)^2 + (y2 - y1)^2]

For the points (-2, -1) and (6, 8), the distance formula becomes:

Distance = √[(6 - (-2))^2 + (8 - (-1))^2]
= √[(6 + 2)^2 + (8 + 1)^2]
= √[8^2 + 9^2]
= √[64 + 81]
= √145
≈ 12.04

Therefore, the distance between the points (-2, -1) and (6, 8) is approximately 12.04.

To find the midpoint of the line segment with the given endpoints (4, 5) and (-10, -5), we can use the midpoint formula:

Midpoint = ( (x1 + x2)/2, (y1 + y2)/2)

For the given points, the midpoint formula becomes:

Midpoint = ( (4 + (-10))/2, (5 + (-5))/2)
= ( (-6)/2, (0)/2)
= ( -3, 0)

Therefore, the midpoint of the line segment with the given endpoints (4, 5) and (-10, -5) is (-3, 0).

Answer 2

Find the midpoint of the line segment with the given endpoints.
(-1, -9), (5, -1)

Answer 3

To find the midpoint of the line segment with the given endpoints (-1, -9) and (5, -1), we can use the midpoint formula:

Midpoint = ( (x1 + x2)/2, (y1 + y2)/2)

For the given points, the midpoint formula becomes:

Midpoint = ( (-1 + 5)/2, (-9 + (-1))/2)
= (4/2, (-10)/2)
= (2, -5)

Therefore, the midpoint of the line segment with the given endpoints (-1, -9) and (5, -1) is (2, -5).

Answer 4

Part E - Converting Standard Form to Slope-Intercept Form
Write each equation in slope-intercept form.
21.x+y=7
22.5x + 2y = -2
23. 2х - 4y = 28
24.x - 4y=0

Answer 5

To convert the equations from standard form to slope-intercept form, which is in the form y = mx + b, where m is the slope and b is the y-intercept, we will rearrange the given equations.

21. x + y = 7

To convert it to slope-intercept form, we need to isolate y. We can do this by subtracting x from both sides:

y = -x + 7

So, the equation in slope-intercept form is y = -x + 7.

22. 5x + 2y = -2

To convert it to slope-intercept form, we need to isolate y. We can do this by subtracting 5x from both sides:

2y = -5x - 2

Next, divide each term by 2:

y = (-5/2)x - 1

So, the equation in slope-intercept form is y = (-5/2)x - 1.

23. 2x - 4y = 28

To convert it to slope-intercept form, we need to isolate y. We can do this by subtracting 2x from both sides:

-4y = -2x + 28

Next, divide each term by -4:

y = (1/2)x - 7

So, the equation in slope-intercept form is y = (1/2)x - 7.

24. x - 4y = 0

To convert it to slope-intercept form, we need to isolate y. We can do this by subtracting x from both sides:

-4y = -x

Next, divide each term by -4:

y = (1/4)x

So, the equation in slope-intercept form is y = (1/4)x.