Q) Point P(x, y) is equidistant from points A(5, 1) and B(1,5). Prove that x = y. Ans: Let’s draw the diagram to solve: Given that PA = PB Hence, PA2 = PB2 (x – 5)2 + (y – 1)2 = (x – 1)2 + (y – 5)2 – 10 x – 2y = – […]
Point P(x, y) is equidistant from points A(5, 1) and B(1, 5). Prove that x = y. Read More »
Q) The line segment joining the points A(4,-5) and B(4,5) is divided by the point P such that AP : AB = 2 : 5. Find the coordinates of P. Ans: Let’s draw the diagram to solve: Given that (AB = AP + PB) by cross multiplication, we get: 5 AP = 2 (AP
Q) Jagdish has a field which is in the shape of a right angled triangle AQC. He wants to leave a space in the form of a square PQRS inside the field for growing wheat and the remaining for growing vegetables (as shown in the figure). In the field, there is a pole marked as
Jagdish has a field which is in the shape of a right angled triangle AQC. Read More »
Q) If Q(0,1) is equidistant from P(5,-3) and R (x,6), find the values of x. Ans: since the Point Q is equidistant, then Distance between P & Q = Distance between R & Q (5-0) 2 + (-3-1) 2 = (x-0)2 + (6-1)2 or 25 +16 = x2 + 25 or x2 = 16
If Q(0,1) is equidistant from P(5,-3) and R (x,6), find the values of x. Read More »
Q) Show that the points (- 2, 3), (8, 3) and (6, 7) are the vertices of a right-angled triangle. Ans: Let’s plot these points on graph, we get: Step 1: Now for a Δ ABC to be an right angled triangle, required condition is: AB2 = AC2 + BC2 Step 2: Let’s calculate the
Q) Solve the pair of equations x = 5 and y = 7 graphically. Ans: Here is the answer to this question: For a detailed answer to this question, please refer to the following question and its solution: (click on the link on the question) Solve the pair of equations x = 3 and y
Solve the pair of equations x = 5 and y = 7 graphically. Read More »
Q) The centre of a circle is (2a, a-7). Find the values of ‘a’ if the circle passes through the point (11,-9). Radius of the circle is 5√2cm. Ans: Let’s find out radius of the circle by co-ordinate method. Therefore, (2a – 11)2 + (a -7 + 9)2 = (5√2 )2 or (4a2 + 121
Q) Using graphical method, find whether following system of linear equations x = 0 and y = – 3 is consistent or not. Ans: Draw graph for y = – 3 and x = 0. As y = – 3 is intersecting x = 0 at (0,-3); So, system of equations is consistent.
Q) If (-5,3) coordinates and (5,3) are two vertices of an equilateral triangle, then find of the third vertex, given that origin lies inside the triangle. (Take √3 = 1.7) Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Let the third vertex be (x, y)Hence, 3 vertex of the triangle will be A (-5,3) B (5,3) C
Q) Solve the pair of equations x = 3 and y = – 4 graphically. Ans: VIDEO SOLUTION STEP BY STEP SOLUTION Step 1: Lets plot both the equations on the graph. Step 2: Increase till these lines intersect each other. We get the intersection point as (3,-4) Since the lines are intersecting at (3,
Solve the pair of equations x = 3 and y =- 4 graphically. Read More »