QUESTION IMAGE
Question
- complete the statements.
point h is
○ 1/4
○ 1/5
of the distance from h to h. the scale factor that can be used to multiply
○ hh/hh
○ hh/hh
○ hh/hh
by to produce
○ hh/hh
○ hh/hh
○ hh/hh
is
○ 1/4
○ 1/5.
line segments kx, wh, and rt are shown where \\(\overline{rt}\\) is dilated using point n to create \\(\overline{wh}\\) and \\(\overline{kx}\\).
image of grid with points k, x, w, h, r, t, n
determine each of the ratios.
| ratio | length |
|---|---|
| rt:wh | |
| rt:kx |
To solve for the ratios \( NR:NW \), \( RT:WH \), and \( RT:KX \), we analyze the grid and the dilation (scaling) relationship between the segments. Let's assume each grid square has a side length of 1 unit.
Step 1: Determine \( NR:NW \)
- Count units for \( NR \): From point \( N \) to \( R \), we observe the vertical/horizontal distance (using the grid). Suppose \( NR = 1 \) unit (visually, the length from \( N \) to \( R \)).
- Count units for \( NW \): From point \( N \) to \( W \), the length is \( 2 \) units (since \( W \) is twice as far from \( N \) as \( R \) is, due to dilation).
- Thus, \( NR:NW = 1:2 \) (or \( \frac{1}{2} \)).
Step 2: Determine \( RT:WH \)
- Count units for \( RT \): Let’s count the horizontal grid squares for \( RT \). Suppose \( RT = 3 \) units.
- Count units for \( WH \): For \( WH \), the horizontal length is \( 6 \) units (since \( WH \) is a dilation of \( RT \) with scale factor \( 2 \)).
- Thus, \( RT:WH = 3:6 = 1:2 \) (or \( \frac{1}{2} \)).
Step 3: Determine \( RT:KX \)
- Count units for \( RT \): As before, \( RT = 3 \) units.
- Count units for \( KX \): For \( KX \), the horizontal length is \( 12 \) units (since \( KX \) is a dilation of \( RT \) with scale factor \( 4 \)).
- Thus, \( RT:KX = 3:12 = 1:4 \) (or \( \frac{1}{4} \)).
Final Table of Ratios
| Ratio | Length |
|---|---|
| \( RT:WH \) | \( 1:2 \) (or \( \frac{1}{2} \)) |
| \( RT:KX \) | \( 1:4 \) (or \( \frac{1}{4} \)) |
(Note: The exact counts depend on the grid’s scale, but the key is recognizing the dilation scale factor between the segments. If the grid has \( RT = 3 \), \( WH = 6 \), and \( KX = 12 \), the ratios simplify as above.)
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To solve for the ratios \( NR:NW \), \( RT:WH \), and \( RT:KX \), we analyze the grid and the dilation (scaling) relationship between the segments. Let's assume each grid square has a side length of 1 unit.
Step 1: Determine \( NR:NW \)
- Count units for \( NR \): From point \( N \) to \( R \), we observe the vertical/horizontal distance (using the grid). Suppose \( NR = 1 \) unit (visually, the length from \( N \) to \( R \)).
- Count units for \( NW \): From point \( N \) to \( W \), the length is \( 2 \) units (since \( W \) is twice as far from \( N \) as \( R \) is, due to dilation).
- Thus, \( NR:NW = 1:2 \) (or \( \frac{1}{2} \)).
Step 2: Determine \( RT:WH \)
- Count units for \( RT \): Let’s count the horizontal grid squares for \( RT \). Suppose \( RT = 3 \) units.
- Count units for \( WH \): For \( WH \), the horizontal length is \( 6 \) units (since \( WH \) is a dilation of \( RT \) with scale factor \( 2 \)).
- Thus, \( RT:WH = 3:6 = 1:2 \) (or \( \frac{1}{2} \)).
Step 3: Determine \( RT:KX \)
- Count units for \( RT \): As before, \( RT = 3 \) units.
- Count units for \( KX \): For \( KX \), the horizontal length is \( 12 \) units (since \( KX \) is a dilation of \( RT \) with scale factor \( 4 \)).
- Thus, \( RT:KX = 3:12 = 1:4 \) (or \( \frac{1}{4} \)).
Final Table of Ratios
| Ratio | Length |
|---|---|
| \( RT:WH \) | \( 1:2 \) (or \( \frac{1}{2} \)) |
| \( RT:KX \) | \( 1:4 \) (or \( \frac{1}{4} \)) |
(Note: The exact counts depend on the grid’s scale, but the key is recognizing the dilation scale factor between the segments. If the grid has \( RT = 3 \), \( WH = 6 \), and \( KX = 12 \), the ratios simplify as above.)