Question

6. A line is of length 5 and one end is at the point (1, - 2); if the abscissa of the other end
is 4, prove that its ordinate must be 2 or-6.
7. Prove that the point (-1,2) is the centre of a circle passing through the points (-3,11),​

Answer 1

Step-by-step explanation:

Let AB be the line of length 5 with vertices of A(1,-2) and B(4,y) .

Then, using distance formula

AB= √(X2-X1)^2+(Y2-Y1)^2

5=√(4-1)^2 + (y-(-2)^2)

5=√(3)^2+(y+2)^2

5=√9+y^2+4+4y

5=√y^2+4y+13

squaring both sides , we get

25=y^2+4y+13

y^2+4y-12=0

y^2+6y-2y-12=0

y(y+6)-2(y+6)=0

(y-2)(y+6)=0

y = 2, -6

Hence proved.