Line segment QR is dilated to create line segment Q'R'using the dilation rule Dt, 1.5What is y, the distance between points R and R?3 units4 units6 units9 units

Answer:The distance between R and R' is 3 units ⇒ 1st answerStep-by-step explanation:A dilation is a transformation that produces an image that is the sameshape as the original, but in a different size. If the image is larger than the original figure then dilation is called an enlargement. If the image is smaller than the original figure then the dilationis called a reduction.The image of a line by dilation parallel to the original line if the original line not passes through the center of dilation.Line segment QR is dilated to create line segment Q'R'∴ QR is parallel to Q'R'The factor of dilation is 1.5∴ The length of Q'R' is 1.5 the length of QRIn Δs TRQ and TR'Q'∵ QR // Q'R'∴ m∠TRQ = m∠TR'Q'∴ m∠TQR = m∠TQ'R'∵ ∠T is common in the two triangles∴ ΔTRQ is similar to ΔTR'Q'∴ [tex]\frac{TR'}{TR}=\frac{R'Q'}{RQ}[/tex]∵ [tex]\frac{Q'R'}{QR}=1.5[/tex]∵ TR' = TR + y∵ Tr = 6 units∴ TR' = 6 + y units∵ [tex]\frac{TR'}{TR}=\frac{6+y}{6}[/tex]∴ [tex]1.5=\frac{6+y}{6}[/tex]Multiply both sides by 6∴ 9 = 6 + ySubtract 6 from both sides∴ 3 = y* The distance between R and R' is 3 units