Q) Find the length of the median AD of Δ ABC having vertices A(0, –1), B(2, 1) and C(0, 3). Ans: Let’s plot the points on the graph: Step 1: Let’s understand the layout: If AD is median, it means D lies on line segment BC, and BD = CD Let the coordinates of point D […]
Find the length of the median AD of Δ ABC having vertices A(0, –1), B(2, 1) and C(0, 3). Read More »
Q) In what ratio does the X-axis divide the line segment joining the points(2, – 3) and (5, 6)? Also, find the coordinates of the point of intersection. Ans: Let’s draw the diagram to solve: (i) Ratio of division: We know that the value of y-coordinate on X- axis is always 0 It is given
Q) A garden is in the shape of a square. The gardener grew saplings of Ashoka tree on the boundary of the garden at the distance of 1 m from each other. He wants to decorate the garden with rose plants. He chose a triangular region inside the garden to grow rose plants. In the above
A garden is in the shape of a square. The gardener grew saplings of Ashoka tree Read More »
Q) Ryan, from a very young age, was fascinated by the twinkling of stars and the vastness of space. He always dreamt of becoming an astronaut one day. So he started to sketch his own rocket designs on the graph sheet. One such design is given below : Based on the above, answer the following questions
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)
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 »