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 […]
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: Method 1: Step 1: 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: 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
Prove that A(4, 3), B(6, 4), C(5, 6), D(3, 5) are the vertices of a square ABCD. Read More »
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),
Find the ratio in which the point (- 1, k) divides the line segment joining the points Read More »
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
Draw the graph of the following equations: x + y = 5, x – y = 5, and Read More »
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
Q) ABCD is a rectangle formed by the points A (−1, −1), B (−1, 6), C (3, 6) and D (3, −1). P, Q, R and S are mid-points of sides AB, BC, CD and DA respectively. Show that diagonals of the quadrilateral PQRS bisect each other. Ans: Let’s make a diagram for the given
ABCD is a rectangle formed by the points A (−1, −1), B (−1, 6), C (3, 6) and D (3, −1). Read More »
Q) Find the ratio in which the point (8/5, y) divides the line segment joining the points (1, 2) and (2, 3). Also, find the value of y. ns: Let’s make a diagram for the given question: Let’s consider the point C(8/5, y) divides the line AB in ratio of P : 1 Now, by
Find the ratio in which the point (8/5, y) divides the line segment joining the points Read More »