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more than 1 week ago

To find the equation of the line passing through points X(3,-2) and Y(4,6), we first need to find the slope of the line.

Slope (m) = (y2 - y1) / (x2 - x1)

m = (6 - (-2)) / (4 - 3)

m = 8

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line passing through points X and Y.

y - y1 = m(x - x1)

y - (-2) = 8(x - 3)

y + 2 = 8x - 24

y = 8x - 26

So, the equation of the line passing through points X and Y is y = 8x - 26.

To find points A and B such that AX = XY = BY, we need to find the midpoint of line XY, which is also the point A and B.

Midpoint formula:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

For points X(3,-2) and Y(4,6):

x = (3 + 4) / 2 = 3.5

y = (-2 + 6) / 2 = 2

Therefore, the coordinates of points A and B are A(3.5, 2) and B(3.5, 2).

Slope (m) = (y2 - y1) / (x2 - x1)

m = (6 - (-2)) / (4 - 3)

m = 8

Now that we have the slope, we can use the point-slope form of the equation of a line to find the equation of the line passing through points X and Y.

y - y1 = m(x - x1)

y - (-2) = 8(x - 3)

y + 2 = 8x - 24

y = 8x - 26

So, the equation of the line passing through points X and Y is y = 8x - 26.

To find points A and B such that AX = XY = BY, we need to find the midpoint of line XY, which is also the point A and B.

Midpoint formula:

x = (x1 + x2) / 2

y = (y1 + y2) / 2

For points X(3,-2) and Y(4,6):

x = (3 + 4) / 2 = 3.5

y = (-2 + 6) / 2 = 2

Therefore, the coordinates of points A and B are A(3.5, 2) and B(3.5, 2).

Google Gemini AI

more than 1 week ago

The equation of the line passing through points X(3,-2) and Y(4,6) is:

```

y - (-2) = (6 - (-2)) / (4 - 3) - (x - 3)

y + 2 = 8 / 1 - (x - 3)

y = 8x - 26

```

The line in the opposite direction has the same slope but a different y-intercept. The equation of this line is:

```

y - 6 = -(8 / 1) - (x - 4)

y = -8x + 42

```

To find the coordinates of A and B, we need to find where the two lines intersect. Solving the system of equations:

```

y = 8x - 26

y = -8x + 42

```

gives us the point of intersection:

```

x = 3, y = 4

```

So,

Anonymous

more than 1 week ago

the value of log2 16 is

Collins Benton

more than 1 week ago

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