Question

Case Study : The houses of four friends are located by point A,B,P and Q shown in figure + A B If coordinates of A(4, -1) and B(-2, -3) with respect to coordinate axes are known and Panda trisect the AB, then answer the following questions: 46. Coordinates of P are 02.) (D) (2) (1) (-2,5 23) 47. Coordinates of Q are 000,-) (m) (0,3) (iv) (0,1) (m) (,0) 48. Distance PQ = (i) 40 units (units (iv) (-2,5 40 (iv) units units 1 40 3 49. Distance AB = (iv) units units (in units 40 3 (i) 40 units (iv) AP 50. Distance AB = PQ (iii) 13PQ ( (ii) 3 (1) 3 PQ X-4​

Answer 1

Answer:

D) (2) (1) (-2,5 23) 47. Coordinates of Q are 000,-) (m) (0,3) (iv) (0,1) (m) (,0) 48. Distance PQ = (i) 40 units (units (iv) (-2,5 40 (iv) units units 1 40 3 49. Distance AB = (iv) units units (in units 40 3 (i) 40 units (iv) AP 50. Distance AB = PQ (iii) 13PQ ( (ii) 3 (1) 3 PQ X-4

Answer 2

Given -

The houses of four friends are located by point A,B,P,Q

If coordinates of A(4, -1) and B(-2, -3) with respect to coordinate axes are known and Panda trisect the AB

To find -

Coordinates of P

Coordinates of Q

Distance PQ

Distance AB

Distance AB

Solution-

46.Coordinates of P:

Panda trisects the line segment AB, which means that point P is located at 1/3 of the distance from A to B. We can use the midpoint formula to find the coordinates of P:

P = ((x1+x2)/2, (y1+y2)/2)

where x1,y1 are the coordinates of point A and x2,y2 are the coordinates of point B.

So, P = ((4+(-2))/2, (-1+(-3))/2) = (1, -2)

47.Coordinates of Q:

Panda trisects the line segment AB, which means that point Q is located at 2/3 of the distance from A to B. We can use the midpoint formula to find the coordinates of Q:

Q = ((2x2+x1)/3, (2y2+y1)/3)

where x1,y1 are the coordinates of point A and x2,y2 are the coordinates of point B.

So, Q = ((2*(-2) + 4)/3, (2*(-3) + (-1))/3) = (0, 1)

48.Distance PQ:

We can use the distance formula to find the distance between P and Q:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

where x1,y1 are the coordinates of point P and x2,y2 are the coordinates of point Q

So, d = sqrt((0-1)^2 + (1-(-2))^2) = sqrt(1 + 9) = sqrt(10) = 3.16 units

49.Distance AB:

We can use the distance formula to find the distance between A and B:

d = sqrt((x2-x1)^2 + (y2-y1)^2)

where x1,y1 are the coordinates of point A and x2,y2 are the coordinates of point B.

So, d = sqrt((-2-4)^2 + (-3-(-1))^2) = sqrt(16 + 4) = sqrt(20) = 4.47 units

50.Distance AB = PQ:

It is not necessarily true that Distance AB = PQ. The distance between two points can be calculated by the distance formula. The value of AB and PQ are calculated by the above formulas, it is not equal. It depends on the coordinates of the given points.

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