Question

Q. Plot a line segment PQ with end-points P(6, 3) and Q06, 15) and rotate point Q about point P by 90° in a clockwise direction to form its image Qj. Write the coordinates of point Q1.
chapter - symmetry, reflection and rotation

pls help me out ​

Answer 1

Step-by-step explanation:

Let the point A(x,y) which lies on line joining P(6,−6) and Q(−4,−1) such that PA/PQ=2/5

Line segment PQ is divided by the point A in the ratio 2:3.

Step 1: Find coordinates of A(x,y)

x=

m

1

+m

2

m

1

x

2

+m

2

x

1

x=(2(−4)+3(6))/(2+3)

=(−8+18)/5

=10/5=2

y=

m

1

+m

2

m

1

y

2

+m

2

y

1

y=(2(−1)+3(−6))/5

=(−2−18)/5

=−20/5

=−4

Step 2: Point A also lies on the line 3x+k(y+1)=0

3(2)+k(−4+1)=0

6−3k=0

or k=2.