Question

Answer the following questions :
1. Find the distance to the point (2, 3) from the origin.
2. Show that the points (-1, 7), (3, -5) and (4, -8) are collinear.
3.If p(x, y) is equidistant from (2,3) and (-2, -3), then write the relation between x and y.
4.Find the perimeter of the triangle whose vertices are (3, 2), (2, -3) and (0,0).
5.Show that the points (-1, -8), (4,-6), (2,-1), (-3,-3) taken in order form a square.​

Answer 1

Answer:

1. d= √(x2-x1)^2 +(y2-y1)^2

(2,3) origin =(0,0)

let 2 be x1 and 3 be y1 and 0 be x2 and 0 be y2

√(0-2)^2 + (0-3)^2

√(-2)^2 +(-3)^2

√4+9

=√13

3.605

Therefore the answer is 3.605

2. 1/2| x1(y2 - y3) +x2 (y3 - y1) + x3 (y1- y2)|

(-1,7) (3,-5) (4,-8)

(x1,y1)(x2,y2)(x3,y3)

1/2| -1 (-5 +8) + 3 (-8 -7) + 4 (7 +5)|

1/2| 5-8-24-21+28+20|

1/2| 53 -53 |

1/2| (0)

1/2*0

0/2

=0

Therefore the points are collinear.

Answer 2

Its form a square

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