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Find
1-The mid point
2-The slop
3-The length
4 - The equation

Find 1-The mid point 2-The slop 3-The length 4 - The equation-example-1
User Dimgold
by
7.8k points

1 Answer

2 votes

Answer:

1, the mid point

The midpoint of a line segment with endpoints (x1, y1) and (x2, y2) can be found using the midpoint formula:

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

Substituting the given endpoints (4, -4) and (0, 9), we get:

midpoint = ((4 + 0) / 2, (-4 + 9) / 2) = (2, 2.5)

Therefore, the midpoint of the line segment with endpoints (4, -4) and (0, 9) is (2, 2.5).

2, the slope

The slope of the line passing through the points (4, -4) and (0, 9) can be found using the formula:

slope = (y2 - y1) / (x2 - x1)

where (x1, y1) and (x2, y2) are the coordinates of the two points.

Substituting the given coordinates, we get:

slope = (9 - (-4)) / (0 - 4) = 13 / (-4) = -3.25

Therefore, the slope of the line is -3.25.

3, the length

The length of the line passing through the points (4, -4) and (0, 9) can be found using the distance formula:

distance = sqrt((x2 - x1)^2 + (y2 - y1)^2)

Substituting the given coordinates, we get:

distance = sqrt((0 - 4)^2 + (9 - (-4))^2) = sqrt(16 + 169) = sqrt(185)

Therefore, the length of the line is sqrt(185).

4, the equation

The equation of the line passing through the points (4, -4) and (0, 9) can be found using the point-slope form of the equation of a line:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is one of the points.

Substituting the given slope and one of the points, we get:

y - (-4) = -3.25(x - 4)

Simplifying, we get:

y + 4 = -3.25x + 13

y = -3.25x + 9

Therefore, the equation of the line passing through the points (4, -4) and (0, 9) is y = -3.25x + 9.

User Lindsay Winkler
by
7.5k points

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