Respuesta :
Answer:
Option B is correct i.e., M'(-6,9) and N'(3,9).
Step-by-step explanation:
Given: ΔMNP mapped in graph ⇒ coordinates of vertices are M(-4,6), N(2,6) & P(-1,1) and scale factor of dilation is 1.5 .i.e., 1.5(x,y) ⇒ (1.5x,1.5y)
ΔMNP dilated to ΔM'N'P'
To Find: Coordinates of M' &N'
since, scale factor of dilation is 1.5.
we get coordinates of M' by multiplying coordinates of M
⇒1.5 M(-4,6) = M'(1.5×(-4), 1.5×6)
=M' (-6,9)
similalrly coordinates of N' by multiplying coordinates of N
⇒1.5 N(2,6) = N'(1.5×2, 1.5×6)
=N' (3,9)
The coordinates of the endpoints of segment M'N' is M'(-6,9) and N'(3,9)
∴Option B is correct.
The correct option for the coordinates of end point of line segment is [tex]\fbox{\begin\\\ \bf option (b)\\\end{minispace}}[/tex].
Further Explanation:
Calculation:
The coordinate of the point [tex]P,M,N[/tex] can be obtained from the given Graph.
The coordinate of the point [tex]P[/tex] of [tex]\triangle\text{PMN}[/tex] is [tex](-1,1)[/tex].
The coordinate of the point [tex]N[/tex] of a triangle [tex]\triangle\text{PMN}[/tex] is [tex](2,6)[/tex].
The coordinates of the point [tex]M[/tex] of a triangle [tex]\triangle\text{PMN}[/tex] is [tex](-4,6)[/tex].
The image of triangle is created by the given rule,
[tex]\boxed{1.5(x,y)\rightarrow(1.5x,1.5y)}[/tex]
The new image of [tex]\triangle\text{PMN}[/tex] is [tex]\triangle\text{M'N'P'}[/tex].
The new coordinate of [tex]P[/tex] that is [tex]P'[/tex] is obtained as,
[tex]\boxed{\begin{aligned}1.5(x,y)&\rightarrow(1.5x,1.5y)\\1.5(-1,1)&\rightarrow(-1.5,1.5)\end{aligned}}[/tex]
The new coordinate of [tex]M[/tex] that is [tex]M'[/tex] is obtained as,
[tex]\boxed{\begin{aligned}1.5(x,y)&\rightarrow(1.5x,1.5y)\\1.5(-4,6)&\rightarrow(-6,9)\end{aligned}}[/tex]
The new coordinate of [tex]N[/tex] that is [tex]N'[/tex] is obtained as,
[tex]\boxed{\begin{aligned}1.5(x,y)&\rightarrow(1.5x,1.5y)\\1.5(2,6)&\rightarrow(3,9)\end{aligned}}[/tex]
Therefore, the coordinate for point [tex]M'[/tex] is [tex](-6,9)[/tex] and the coordinate for the point [tex]N'[/tex] is [tex](3,9)[/tex].
Thus, the correct option for the coordinates of end point of line segment is [tex]\fbox{\begin\\\ \bf option (b)\\\end{minispace}}[/tex].
Learn more:
1. A problem on triangle: https://brainly.com/question/7437053
2. A problem on transformation of triangle https://brainly.com/question/2992432
Answer details:
Grade: High school
Subject: Mathematics
Chapter: Triangle
Keywords: Equations, Triangle, dilate, Translate, image, size, x coordinate, y coordinate, shifted position endpoints, line segment, shifting, 1.5(x,y)=(1.5x,1.5y).
