Quiz- 4

Distance = √(〖(-5)〗^2+0^2 )
= 5

The coordinates can be calculated using formulae,
X = (2x3+ 3x2)/(2+3) = 12/5
Y = (2x6+ 3x5)/(2+3) = 27/5

Solution

The point lies in the first quadrant

solution:

Centre is the midpoint of PS, hence,
2 = (1+x)/2 = 3
-3 = (4+y)/2 = -10
= (3, -10)

Solution:

Area enclosed by the lines must be zero for all these points to be collinear
Area = 1/2 [7 (1-p) + 5 (p + 2) + 3 (-2-1)]
= 7 – 7p + 5p +10 -9
P= 2

Solution:

Formula to calculate area = 1/2 [1 (5 +5) + 2 (-5 - 2) -2 (2 - 5) ] = 1

Solution:

Let us assume the ratio is m: n

Coordinate of the intersection becomes 

X= (3m+ 2n)/(m+n)

Y= (7m- 2n)/(m+n) 

Substituting the values in the given equation, we get

2 ((3m+ 2n)/(m+n)) + (7m- 2n)/(m+n) - 4 = 0

Therefore, m: n= 2: 9

Solution:
The midpoint can be calculated as,
(3 +a)/2, 4
Substituting these values in the equation, we get
(3+a)/2 -4 -20 =0
3+a =48
A= 45

Solution:

Centroid of the triangle = ( (x1+x2+x3)/3 , (y1+y2+y3)/3 )

= (3-7+10)/3, (-5+4-2)/3

= (2, -1)

Solution:
Considering the points to be A, B, C, and D,
The midpoint of AC = Midpoint of BD
(x+1)/2 , (6+2)/2 = (4+3)/2, (y+5)/2
= (x+1)/2 = 7/2 and (6+2)/2 = (y+5)/2
X+1 = 7 and 8 = y+5
X= 6, and y = 3