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
Q) Using graphical method, solve the following system of equations : 3 x – 2 y = 10 and 5 x + 3 y = 4 Ans:Â 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
Q) 22. Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5). Ans: Step 1: Let’s plot the points on the graph: Step 2:Â Given vertices are A(1, 0), B(- 5, 0) and C(- 2, 5). Let’s find out lengths of all the sides: We know that the
Find the type of triangle ABC formed whose vertices are A(1, 0), B(-5, 0) and C(-2, 5). Read More »
Q) In what ratio is the line segment joining the points (3, – 5) and (- 1, 6) divided by the line y = x ? Ans:Â Method 1: Step 1:Â Â Now, 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)
Q) A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC. Find length of its median BE. Ans:Â Let’s plot the points on the graph: Step 1:Â Â To draw median BE, point E lies on AC Let’s consider the coordinates of E are (x, y) Since E is the midpoint of A C, we