Question

1.what is the length of the segment joining 3,6 and -2,-6

Answer 1

1.what is the length of the segment joining 3,6 and -2,-6 : 13 units

2.what is the center of the circle (x+6)^2+(y-8)^2=144 => (-6,8)

3.what is the slope of the line 3y+2x-6=0=> -2/3

Step-by-step explanation:

1.what is the length of the segment joining (3,6) and (-2,-6)?

Let

(x1,y1) = (3,6)

(x2,y2) = (-2,-6)

The length of a segment is given by:

$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\\Putting\ values\\d = \sqrt{(-2-3)^2+(-6-6)^2}\\d = \sqrt{(-5)^2+(-12)^2}\\= \sqrt{25+144}\\= \sqrt{169}\\=13\ units$

2.what is the center of the circle (x+6)^2+(y-8)^2=144

The equation of circle is given by:

$(x-h)^2+(y-k)^2 = r^2$

Here, h and k are the coordinates of centre of circle

x - h = x+6

-h = 6

h = -6

y - 8 = y - k

-8 = - k

k = 8

So,

The center of circle is: (-6,8)

3.what is the slope of the line 3y+2x-6=0

We have to convert the equation in slope-intercept form to find the slope

Slope-intercept form is:

y = mx+b

Now,

$3y+2x-6=0\\3y+2x = 6\\3y = -2x+6$

Dividing both sides by 3

$\frac{3y}{3} = -\frac{2}{3}x+\frac{6}{3}\\y = -\frac{2}{3}x + 2$

In slope-intercept form, the co-efficient of x is the slope of the line so

m = -2/3

Keywords: Coordinate geometry, Slope

Learn more about coordinate geometry at:

• brainly.com/question/2821386
• brainly.com/question/2860697

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