Find the distance between each pair of points.
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)
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).
Find the midpoint of the line segment with the given endpoints.
(-1, -9), (5, -1)
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).
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
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.
To find the distance between two points, we can use the distance formula:
d = sqrt((x2 - x1)^2 + (y2 - y1)^2)
Let's calculate the distance between the points (-2, -1) and (6, 8):
d = sqrt((6 - (-2))^2 + (8 - (-1))^2)
= sqrt((6 + 2)^2 + (8 + 1)^2)
= sqrt(8^2 + 9^2)
= sqrt(64 + 81)
= sqrt(145)
≈ 12.04
Therefore, the distance between the points (-2, -1) and (6, 8) is approximately 12.04.
To find the midpoint of a line segment, we can use the midpoint formula:
Midpoint = ((x1 + x2) / 2, (y1 + y2) / 2)
Let's find the midpoint of the line segment with the endpoints (4, 5) and (-10, -5):
Midpoint = ((4 + (-10)) / 2, (5 + (-5)) / 2)
= ( -6 / 2, 0 / 2 )
= (-3, 0)
Therefore, the midpoint of the line segment with the endpoints (4, 5) and (-10, -5) is (-3, 0).
To find the distance between the points (-2,-1) and (6,8), you can use the distance formula.
The distance between two points (x1, y1) and (x2, y2) is given by the formula:
d = √((x2 - x1)² + (y2 - y1)²)
Substituting the given values, we have:
d = √((6 - (-2))² + (8 - (-1))²)
Simplifying this expression, we get:
d = √(8² + 9²)
d = √(64 + 81)
d = √145
d ≈ 12.0 (rounded to the nearest tenth)
Therefore, the distance between the points (-2,-1) and (6,8) is approximately 12.0.
To find the midpoint of the line segment with endpoints (4, 5) and (-10, -5), you can use the midpoint formula.
The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) is given by the formula:
M = ((x1 + x2)/2, (y1 + y2)/2)
Substituting the given values, we have:
M = ((4 + (-10))/2, (5 + (-5))/2)
Simplifying this expression, we get:
M = ((-6)/2, 0/2)
M = (-3, 0)
Therefore, the midpoint of the line segment with endpoints (4, 5) and (-10, -5) is (-3, 0).