Coordinate geometry 1 questions | form five Pure Advanced Mathematics

Find Coordinate geometry 1 examination questions, form five Pure Advanced Mathematics in acaproso.com

#	Question
1	Show that C(7,-2) and D(1,6) are all equidistant from the line 3x-4y-4=0 Mathematical Calculation
2	Prove that $Mleft ( frac{x_1+x_2}{2}, frac{y_1+y_2}{2} ight )$ is the mid point of the line segment joining $P_1(x_1,y_1)$ and $P_2(x_2,y_2)$ . Mathematical Calculation
3	The end point coordinates of a line segment AB are $A(x_{1},y_{1})$ and $B(x_{2},y_{2})$ . Prove that the coordinates of the point p(x,y) dividing the line segment AB internally in the ratio $lambda :mu$ are given by $p(x,1)=left ( frac{mu x_1 lambda x_2}{mu + lambda}, frac{mu y_1 lambda y_2}{mu + lambda} ight )$ . Mathematical Calculation
4	Find the coordinates of a point dividing the line segment joining Q(-3,6) and R(6,0) internally in the ratio 2:1. Mathematical Calculation
5	The vertices of rectangle ABCD are given by points $A(x_{1},y_{1}), B(x_{2},y_{2}), C(x_{3},y_{3}), and ,D(x_{4},y_{4})$ . derive the formula to calculate the area of the rectangle. Use the formula obtained in part (a) to find the area of the rectangle whose vertices are the points $A(1,1), B(3,5), C(-2,4), and ,D(-1,-5).$ Mathematical Calculation
6	Show that the line 3x-4y+14=0 is a tangent to a circle $x^{2}+y^{2}+4x+6y-3=0$ . Mathematical Calculation
7	If the circles $x^{2}+y^{2}-2y-8=0$ and $x^{2}+y^{2}-24x+hy=0$ cut orthogonally, determine the value of h. Mathematical Calculation
8	Find the equation of the normal line passing through point K(7,4) to the circle whose equation is $x^{2}+y^{2}-4x-6y+9=0$ . Mathematical Calculation
9	Calculate the area of the triangle whose vertices are the points L(3,5), M(4,2) and N(6,3). Mathematical Calculation
10	Find the value of k such that $k(x^{2}+y^{2})+(y-2x+1)(y+2x+3)=0$ is a circle. Hence obtain the center and radius of the resulting circle. Mathematical Calculation