1.what is the length of the segment joining 3,6 and -2,-62.what is the center of the circle (x+6)^2+(y-8)^2=1443.what is the slope of the line 3y+2x-6=0

1.what is the length of the segment joining 3,6 and -2,-6 : 13 units2.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=> -2/3Step-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:[tex]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[/tex]2.what is the center of the circle (x+6)^2+(y-8)^2=144The equation of circle is given by:[tex](x-h)^2+(y-k)^2 = r^2[/tex]Here, h and k are the coordinates of centre of circlex - h = x+6-h = 6 h = -6y - 8 = y - k-8 = - kk = 8So,The center of circle is: (-6,8)3.what is the slope of the line 3y+2x-6=0We have to convert the equation in slope-intercept form to find the slopeSlope-intercept form is: y = mx+bNow,[tex]3y+2x-6=0\\3y+2x = 6\\3y = -2x+6[/tex]Dividing both sides by 3[tex]\frac{3y}{3} = -\frac{2}{3}x+\frac{6}{3}\\y = -\frac{2}{3}x + 2[/tex]In slope-intercept form, the co-efficient of x is the slope of the line som = -2/3Keywords: Coordinate geometry, SlopeLearn more about coordinate geometry at: brainly.com/question/2821386brainly.com/question/2860697#LearnwithBrainly