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Find the coordinate of the line drawn from (6,3) perpendicular to the line joining (4,1) and (8,3).​

User Robouste
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Answer:

Coordinate: (0,15)

Explanation:

To find the equation of the line perpendicular to the line joining (4,1) and (8,3) and passing through the point (6,3), we can follow these steps:

Find the slope of the line joining (4,1) and (8,3).

Slope (m) = (change in y) / (change in x)

Slope (m) = (3 - 1) / (8 - 4)

Slope (m) = 2 / 4

Slope (m) = 1/2

So, the slope of the line joining (4,1) and (8,3) is 1/2.

Now,

Determine the negative reciprocal of the slope.

The negative reciprocal of 1/2 is -2.

Use the point-slope form of a line to find the equation of the perpendicular line.

The point-slope form of a line is given by:

y - y₁ = m(x - x₁)

where:

  • (x₁, y₁) is a point on the line (in this case, (6,3)),
  • m is the slope of the line (in this case, -2).

Substitute the values:

y - 3 = -2(x - 6)

Simplify this equation:

y - 3 = -2x + 12

Add 3 to both sides to isolate y:

y = -2x + 12 + 3

y = -2x + 15

To find the coordinate take any value of x and substitute it this equation and solve it.

If x = 0,

y = -2 × 0 + 15

y = 15

Therefore, one coordinate is (0,15).

Note:

We can find an infinite number of coordinates by substitution of any value of x in the equation y = -2x + 15.

User Pkaleta
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