Q) Find the point(s) on the x-axis which is at a distance of √41 units from the point (8, -5). Ans: Let the point be A and coordinates of this point be (x, y) Since any point on X-axis will have y = 0, Hence, the coordinates of the point A will be (X, 0) […]
coordinate geometry
Q) Show that the points A(-5,6), B(3, 0) and C( 9, 8) are the vertices of an isosceles triangle. Ans: For a triangle to be an isosceles triangle, its any 2 sides should be equal. Let’s start by calculating length of its sides: We know that the distance between two points P (X1, Y1) and
Q) Solve the following system of linear equations graphically: x + 2 y = 3, 2 x – 3 y + 8 = 0 Ans: Step 1: To plot the equations, let’s first find out the coordinates of points lying on these lines: For line: x + 2 y = 3,, we calculate coordinates of
Solve the following system of linear equations graphically: x+2y = 3, 2x-3y+8 = 0 Read More »
Q) Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is a diameter of the circle. Find the value of y. Also, find the radius of the circle. Ans: (i) value of y: We know that the center is the midpoint of the diameter, Therefore if AB
Points A(–1, y) and B(5, 7) lie on a circle with centre O(2, –3y) such that AB is Read More »
Q) Find a relation between x and y such that the point P(x, y) is equidistant from the points A(7, 1) and B(3, 5). Ans: We know that the distance between two points (X1, Y1) and (X2, Y2) is given by: S = √ [(X2 – X1)2 + (Y2 – Y1)2 ] Now distance between A(7,1)
Find a relation between x and y such that the point P(x, y) is equidistant Read More »
Q) Solve the following system of linear equations graphically: 3 x – y + 1 = 0 x + y = 5 Ans: Step 1: To plot the equations, let’s first find out the coordinates of points lying on these lines: For line: 3 x – y + 1 = 0,, we calculate coordinates of
Solve the following system of linear equations graphically: 3 x – y + 1 = 0 Read More »
Q) Find the ratio in which the line segment joining the points (5, 3) and (–1, 6) is divided by Y-axis. Ans: Method 1: Step 1: By section formula, coordinates of point P (X, Y) which lies between two points (x1, y1), (x2, y2) will be given by: P (X,Y) = here, the point divides
Q) P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment PQ such that PR = 2QR. Ans: Step 1: Given that point point R divides line PQ, so that PR = 2 QR therefore, Point R divides the lines PQ in ratio of 2: 1 Step
P(–2, 5) and Q(3, 2) are two points. Find the coordinates of the point R on line segment Read More »
Q) Using graphical method, solve the following system of equations : 3 x – 2 y = 10 and 5 x + 3 y = 4 Ans: Ans: (i) Solution of the equations: Step 1: Let’s find the points on both lines and plot on the graph paper: a) 3 x – 2 y =
Q) The vertices of Δ ABC are A (- 2, 4), B(4, 3) and C(1, – 6). Find length of the median BD. Ans: Let’s plot the points on the graph: Step 1: To draw median BD, point D lies on AC Let’s consider the coordinates of D are (X, Y) Since D is the midpoint of