23) Write the equation in slope-intercept form of the line that contains (4, -1) and is perpendicular to

Mathematics

1 answer:

Salsk061 [2.6K]3 years ago

8 0

Step-by-step explanation:

Since it is asking for a perpendicular line, we take the reciprocal of the slope in the given equation to use as the slope for the perpendicular line.

In y = x + 2, m = 1. However, for a perpendicular line we flip and multiply by a negative 1.

(Example: If m = 3, we would take the reciprocal of it and it turns into m = -1/3. If m = - 1/4, we would take the reciprocal of it and it turns into m = 4.)

So, the m = 1 turns into a m = -1.

Now, you can use the point (4,-1) to form a point-slope equation first.

y-(-1) = -1(x-4)

Then, use basic algebra to form a slope-intercept form equation.

y + 1 = -x + 4

y = -x +3

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Find the center of the circle that you can circumscribe about DABC.

Vlada [557]

The center of the circle that circumscribe about DABC is $(h,k) = (1, 5)$ .

A circle can be modelled after a expression of the form:

$A\cdot x + B\cdot y + C =-x^{2}-y^{2}$ (1)

We can determine all coefficients by knowing three <em>distinct</em> points on plane.

If we know that $(x_{1}, y_{1}) = (2, 8)$ , $(x_{2}, y_{2}) = (0, 8)$ and $(x_{3}, y_{3}) = (2, 2)$ , then the solution of the system of linear equations is:

$2\cdot A + 8\cdot B + C = -68$ (2)

$8\cdot B + C = -64$ (3)

$2\cdot A + 2\cdot B + C = -8$ (4)

$A = -2, B = -10, C = 16$

Now we proceed to <em>complete</em> squares and factor each resulting perfect square trinomial in order to determine the coordinates of the center of the circle:

$x^{2}+y^{2}-2\cdot x -10\cdot y +16 = 0$