simply add the like terms: 4p -3p +2q -2q = p
Points: (p, q) and (7p, 3q) Midpoint: (4p, 2q) Slope: q/3p Perpendicular slope: -3p/q Perpendicular bisector equation:- => y-2q = -3p/q(x-4p) => qy-2q^2 = -3p(x-4p) => qy-2q^2 = -3px+12p^2 => qy = -3px+12p^2+2q^2 In its general form: 3px+qy-12p^2-2q^2 = 0
4p+7q
5p x 2p = 10p, then 10p / 4p = 2 remainder 2
In its general form it works out as: 3px+qy-12p2-2q2 = 0Improved Answer:-Points:(p, q) and (7p, 3q)Slope: q/3pPerpendicular slope: -3p/qMidpoint: (4p, 2q)Equation: y-2q = -3p/q(x-4p) => yq = -3px+12p2+2q2Perpendicular bisector equation in its general form: 3px+qy-12x2-2q2 = 0
simply add the like terms: 4p -3p +2q -2q = p
Points: (p, q) and (7p, 3q) Midpoint: (4p, 2q) Slope: q/3p Perpendicular slope: -3p/q Perpendicular bisector equation:- => y-2q = -3p/q(x-4p) => qy-2q^2 = -3p(x-4p) => qy-2q^2 = -3px+12p^2 => qy = -3px+12p^2+2q^2 In its general form: 3px+qy-12p^2-2q^2 = 0
4p+7q
5p x 2p = 10p, then 10p / 4p = 2 remainder 2
4p+2q=34 9p+4q=74
In its general form it works out as: 3px+qy-12p2-2q2 = 0Improved Answer:-Points:(p, q) and (7p, 3q)Slope: q/3pPerpendicular slope: -3p/qMidpoint: (4p, 2q)Equation: y-2q = -3p/q(x-4p) => yq = -3px+12p2+2q2Perpendicular bisector equation in its general form: 3px+qy-12x2-2q2 = 0
18 1i 2q 1i 2q -1i,-18 1i -2q 1i -2q -1i,0 1i -2q 18,-a 1i -2q u,-k 1i -2q k,-u 1i -2q a,-18 1i -2q 0,-1i 1i -2q -a,-1s 1i -2q -k,-26 1i -2q -u,-2g 1i -2q -18,k 1i 2q k,u 1i 2q a,18 1i 2q 0,1i 1i 2q -a,1s 1i 2q -k,26 1i 2q -u,2g 1i 2q -18,2q -42 2q -1i,2q -42 -2q -42 -2q -18,0 -42 -2q -3o,-a -42 -2q -3e,-k -42 -2q -34,-u -42 -2q -2q,-18 -42 -2q -2g,-1i -42 -2q -26,-1s -42 -2q -1s,-26 -42 -2q -1i,-2g -42 -2q -18,0 -42 2q -3o,a -42 2q -3e,k -42 2q -34,u -42 2q -2q,18 -42 2q -2g,1i -42 2q -26,1s -42 2q -1s,26 -42 2q -1i,2g -42 2q -18,0 1i 0 i4 1s qs,0 i4 -1s qs,0 5k 34 h6,0 5k -2q h6,-1i 1i 2q 1i,2q u a 1i,2q 18 0 1i#-18 -34 -u -34 -k -2q -k -2g -u -26 -18 -26 -1i -2g -1i -2q -18 -34,u -34 18 -34 1i -2q 1i -2g 18 -26 u -26 k -2g k -2q u -34,-1i -a -u 0 18 0 1s -a,0 -1i -a -u 0 -u,-a 1i 0 1s#B 0 -3e 8e,B 0 u 2q,G -1s -34 9r,G -1s k 71,G 1s k 47,G 1s -34 1d,G 0 -42 b8,G -2q -18 8e,G 0 1i 5k,G 2q -18 2q
First find the midpoint the slope and the perpendicular slope of the points of (p, q) and (7p, 3q) Midpoint = (7p+p)/2 and (3q+q)/2 = (4p, 2q) Slope = (3q-q)/(7p-p) = 2q/6p = q/3p Slope of the perpendicular is the negative reciprocal of q/3p which is -3p/q From the above information form an equation for the perpendicular bisector using the straight line formula of y-y1 = m(x-x1) y-2q = -3p/q(x-4p) y-2q = -3px/q+12p2/q y = -3px/q+12p2/q+2q Multiply all terms by q and the perpendicular bisector equation can then be expressed in the form of:- 3px+qy-12p2-2q2 = 0
2q ÷ q = 2
A line with slope m has a perpendicular with slope m' such that:mm' = -1→ m' = -1/mThe line segment with endpoints (p, q) and (7p, 3q) has slope:slope = change in y / change in x→ m = (3q - q)/(7p - p) = 2q/6p = q/3p→ m' = -1/m = -1/(q/3p) = -3p/qThe perpendicular bisector goes through the midpoint of the line segment which is at the mean average of the endpoints:midpoint = ((p + 7p)/2, (q + 3q)/2) = (8p/2, 4q/2) = (4p, 2q)A line through a point (X, Y) with slope M has equation:y - Y = M(x - x)→ perpendicular bisector of line segment (p, q) to (7p, 3q) has equation:y - 2q = -3p/q(x - 4p)→ y = -3px/q + 12p² + 2q→ qy = 12p²q + 2q² - 3pxAnother Answer: qy =-3px +12p^2 +2q^2
Let f(X)=2X2+6X+3 So f(-p)=f(2q) or 2p2-6p+3=8q2+12q+3 or p2-3p=4q2+6q or p2-4q2=3p+6q or (p+2q)(p-2q)=3(p+2q) so p-2q=3
First find the mid-point of the line segment which will be the point of intersection of the perpendicular bisector. Then find the slope or gradient of the line segment whose negative reciprocal will be the perpendicular bisector's slope or gradient. Then use y -y1 = m(x -x1) to find the equation of the perpendicular bisector. Mid-point: (7p+p)/2 and (3q+q)/2 = (4p, 2q) Slope or gradient: 3q-q/7p-p = 2q/6p = q/3p Slope of perpendicular bisector: -3p/q Equation: y -2q = -3p/q(x -4p) y = -3px/q+12p2/q+2q Multiply all terms by q to eliminate the fractions: qy = -3px+12p2+2q2 Which can be expressed in the form of: 3px+qy-12p2-2q2 = 0