# coordinate geometry

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

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:  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

Q) In what ratio is the line segment joining the points (3, – 5) and (- 1, 6) divided by the line y = x ? Ans: Let’s plot the points on the graph: Step 1:  Now, by section formula, coordinates of point P (X, Y) which lies between two points (x1, y1), (x2, y2) will be

Q) A(3, 0), B(6, 4) and C(-1, 3) are vertices of a triangle ABC. Find length of its median BE. Ans: Let’s plot the points on the graph: Step 1:  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

Q) Prove that A(4, 3), B(6, 4), C(5, 6), D(3, 5) are the vertices of a square ABCD. Ans: Let’s plot the points on the graph: Step 1: Now for a quadrilateral ABCD to be a square, required conditions are: i) its all four sides should be equal i.e. AB = BC = CD = AD

Q) Show that the points (-3, – 3), (3, 3) and (-3√3, 3√3) are the vertices of an equilateral triangle. Ans: Let’s consider the points given (-3, – 3) is A, (3, 3) is B and (-3√3,3√3) is C. Now for a triangle to be an equilateral triangle, required condition is that its all three

Q) Find the ratio in which the point (- 1, k) divides the line segment joining the points (- 3, 10) and (6, – 8). Also, find the value of k. Ans:  Step 1: Finding the division ratio: Now, by section formula, coordinates of point P (X, Y) which lies between two points (x1, y1),

Q) Draw the graph of the following equations: x + y = 5, x – y = 5, and (i) find the solution of the equations from the graph. (ii) shade the triangular region formed by the lines and the y-axis. Ans: (i) Solution of the equations: Step 1: Let’s find the points on both

Q) Using graphical method, solve the following system of equations : 3x + y + 4 = 0 and 3 x – y + 2 = 0 Ans:  Step 1: Let’s try to find the intersection points on X – axis and Y – axis for each of the lines: A. For linear equation 3

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