Question

Select from the drop-down menus to correctly complete each statement.

Triangle ABC can be mapped onto Triangle DEF with a reflection across the____, followed by a translation of 1 unit to the right and 3 units up, and a dilation centered at the origin with a scale factor of____.

FIRST BLANK: x-axis | y-axis
SECOND BLANK: 0.5 |2

Answer 1

Answer with explanation:

→When a triangle is reflected across,x axis or y axis, the perpendicular distance of each of the vertices from ,either of axis chosen for reflection, on both sides of axis from the vertices is same.

→When,  ΔABC, having coordinates of vertices, A(-1,3), B(-4,3) and C(-4,6) ,is reflected across ,y axis ,the vertices of New triangle will transform to or changes to, X(1,3),Y(4,3) and Z(4,6).

→→Now, ΔX Y Z is translated by 1 unit to the right and 3 units up,then coordinates of vertices of ΔPQR  , will be

 $X(1,3)_{+1,+3}=P(1+1,3+3}=P(2,6)\\\\Y(4,3)_{+1,+3}=P(4+1,3+3}=Q(5,6)\\\\Z(4,6)_{+1,+3}=P(4+1,6+3}=R(5,9)$

→Now,if  the triangle X(1,3), Y(4,3), Z(4,6), is dilated by a scale factor of ,2 units , then, Vertices of Δ DEF, will be

X(2×1,2×3)→D(2,6)

Y(2×4,2×3)→E(8,6)

Z(2×4,2×6)→F(8,12)

FIRST BLANK: → y-axis

SECOND BLANK:→2 (Scale factor)