coordinate geometry homework 9 23

Question: Calculate the distance between A (7, 3) and B on the x-axis whose abscissa is 11. [2 Mark] Answer: The co-ordinates of B are (11, 0). (on the x-axis, y = 0, abscissa = x-coordinate = 11)..

Question: Prove that the points A(-5, 4), B(-1, -2) and C(5, 2) are the vertices of an isosceles right angled triangle. Find the Coordinates of D so that ABCD is a square. [3 Mark] Answer: If ABC is a right angled triangle, by Pythagoras theorem, AB 2 + BC 2 = AC 2 an..

Question: Prove that A (-4, 3), B (0, 9), C (-3, 11) and D (-7, 5) form a parallelogram ABCD. [3 Mark] Answer: If ABCD are the vertices of the parallelogram, then their opposite sides are equal in length and parallel. AB = CD and BC = AD ..

Question: In the given figure, P(3,1) is a point on the line segment AB such that AP:PB = 2:3. Find the co-ordinates of A and B. [3 Mark] Answer: Since A is a point on x-axis, let the co-ordinates of A be (x,0). Since B is a point on y-axis, let the ..

The position of the point P in a plane in the rectangular co-ordinate system is determined as follows: Draw PA and PB perpendicular to XX' and YY'. The segment OA = a measures the distance along the x-axis (the x-coordinate and the perpendicular distance AP = OB = b ( paralle..

Question: Find the co-ordinates of the point of intersection of the medians of triangle ABC, given A = (-2,3), B = (6,7), C = (4,1). [3 Mark] Answer: In ABC, AD is the median. D is the midpoint of..

Question: The line segment joining A(2,3) and B(6,-5) is intersected by the x-axis at point K. Write down the ordinate of K. Hence find the ratio in which K divides AB. [3 Mark] Answer: The point K is on the x-axis. Therefore, the ordinate of K is 0. Let the co-ordi..

D is (1, -2). C divides PQ in the ratio 2:3. C is (2,-4). B divides PQ in the ratio 3:..

Distance between the two points ..