I need help on 1 ac Text book section 21 to 23 Problerns 1

I need help on 1 a-c

. Text book section 2.1 to 2.3 Problerns 1). The corners of a square are given by the following coordinates The corners ofa square are given by the following coordinates: (-1,1), (-4,5), (2,8), (5,2) a). Determine the equation of the circle inscribed inside the square. b). Determine the equation of the line parallel to the side from (-1,-1) to (5,2) and through the center of the circle. c). Determine the equation of the line perpendicular to the side from (-1,-1) to (5,2) 2) Consider the line through the points (1.5) and (1,-1) and through the center of the circle. a). Determine the equation of the line. b). Determine the e b). Deternine the equation of the line parallel to the first line and through the point

Solution

coordinates of square are

( -1,-1) , (-4,5) , (2,8) , (5,2)

diameter of the circle is distance between two corners

distance between (-4,5 ) and (2,8)

d = sqrt (x2 - x1)^2 + (y2 - y1)^2

d = 6.71

hence radius of the circle is 6.71 /2 = 3.35

standard equation of circle is given by

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

where h,k is the centre of the circle

we know that circle passes therough mid points of the corners of the square

so finding 2 points through which teh circle passes

mid point of (-4.5) and (-1,-1) = (-5/2 , 2)

mid point of (5,2) and (2,8) = (7/2 , 5 )

centre of the circle would be midpoint of (-5/2 , 2) and (7/2 , 5 )

centre = (1/2 , 7/2)

h = 1/2 , k = 7/2

hence, equation of circle is

(x- 1/2)^2 + ( y - 7/2)^2 = 3.35^2

b) equation of line parallel to (-1,-1) and (5,2)

slope of this line is 1/2

slope of parallel line would be 1/2

hence , equation of line with slope 1/2 and point ( 1/2 , 7/2 )

using y = mx + b and plugging the values of m and x, y

hence equation is

y = 1/2 x +13/4