a) Distance from centre of enlargement (−3,1) to point A(2,−3) is is multiplied by scale factor 2
(x1−(−3))=2(2−(−3))=>x1=7
(y1−1)=2(−3−1)=>y1=−7 A1(7,−7)
b)
(x+2)2+(y−1)2=32
y=−x−1
Points A(2,−3) and A2(x2,y2) lie on the circle
(x+2)2+(y−1)2=32Point A(2,−3) is the point of intersection this circle and the line
y=−x−1 Rotation of center (−2,1) and angle θ=π/6.
The image of the line y=−x−1 is the line
y=−tan(4π−6π)x+b
y=−tan(12π)x+(1−2tan(12π))
Point A2(x2,y2) is the point of intersection the circle
(x+2)2+(y−1)2=32 and the line
y=−tan(12π)x+(1−2tan(12π))
Then
y2=−tan(12π)x2+(1−2tan(12π))
(x2+2)2+(y2−1)2=32 Substitute
(x2+2)2+(−tan(12π)x2−2tan(12π))2=32,
x2>0
x22+4x2+4+tan2(12π)x22+4tan(12π)x2
+4tan2(12π)=32
sec2(12π)x22+4(1+tan(12π))x2
+4sec2(12π)−32=0 D=16+32tan(12π)+16tan2(12π)−16sec4(12π)
+128sec2(12π) Since x2>0
x2=−2cos2(12π)+cos2(12π)4D
y2=−tan(12π)x2+(1−2tan(12π))
Comments
Leave a comment