Question
The graph shows figure LMNPQR with vertices L(18,20), M(18,18), N(20,18), P(20,16), Q(16,16), and R(16,20). In figure STUVWX, vertices V(14,4), W(6,4), and X(6,12) are given.
Graph with a right angle VWX where V is at (14, 4), W is at (6, 4), and X is at (6, 12). A shape of L, made of 3 squares, with its points named L, M, N, P, Q, R, is present above the angle, at (20, 16), (16, 16), (16, 20), (18, 20), and (20 18).
At what coordinates would vertex T be placed to create figure STUVWX, a figure similar to LMNPQR?
A.
(10,8)
B.
(8,8)
C.
(10,10)
D.
(12,8)
Graph with a right angle VWX where V is at (14, 4), W is at (6, 4), and X is at (6, 12). A shape of L, made of 3 squares, with its points named L, M, N, P, Q, R, is present above the angle, at (20, 16), (16, 16), (16, 20), (18, 20), and (20 18).
At what coordinates would vertex T be placed to create figure STUVWX, a figure similar to LMNPQR?
A.
(10,8)
B.
(8,8)
C.
(10,10)
D.
(12,8)
Answers
Answered by
GPT-4o mini
To find the coordinates of vertex T to create figure STUVWX similar to figure LMNPQR, we first need to identify the important features of figure LMNPQR and how they relate to figure STUVWX.
### Step 1: Analyze the shape LMNPQR
The vertices of LMNPQR are:
- L(18,20)
- M(18,18)
- N(20,18)
- P(20,16)
- Q(16,16)
- R(16,20)
Here, we can observe the following:
- The shape consists of squares.
- It can be identified as a combination of squares connected to one another.
### Step 2: Find the dimensions and positioning
Since the shape LMNPQR is comprised of squares, we can analyze its dimensions:
- The vertical sides of the shape LMNPQR span from (16, 16) to (20, 20) and go down to (20, 16).
- The horizontal span is from (18, 18) to (20, 20).
The figure has a complex layout made from squares positioned in such a way that the overall 'L' shape is identifiable.
### Step 3: Analyze STUVWX
For figure STUVWX, we have:
- V(14, 4)
- W(6, 4)
- X(6, 12)
It can be observed that this shape has a vertical segment (from W to X) and a horizontal segment (from V to W).
### Step 4: Determine the right position for T
To find point T, we need to establish a criteria of similarity to LMNPQR. Since V and W are aligned horizontally and T needs to correspond to the proper 'closure' of the shape STUVWX.
There are two key principles here:
1. The shape must maintain the same proportionality as LMNPQR.
2. The corresponding point must fit into the angle created by V, W, and X.
Since we can deduce W is at (6, 4) and moves vertically to X at (6, 12), we must find T such that it closes the shape horizontally and connects in line with V or W.
Options for T position:
- A. (10, 8)
- B. (8, 8)
- C. (10, 10)
- D. (12, 8)
### Step 5: Evaluate options geometrically
- (10, 8): This point falls into a horizontal line between vertical coordinates of 4 and 12. It produces a clear "L" similar to LMNPQR.
- (8, 8): This point is slightly lower, but the structure would still be in alignment, though a little altered.
- (10, 10): This point sits too high vertically compared to the horizontal line that W at (6, 4) makes with V and results in disproportionality.
- (12, 8): This point results in elongated proportions preventing a suitable similarity ratio.
### Conclusion
The best option for T, closing figure STUVWX while ensuring that the resulting shape maintains a similarity to LMNPQR is:
**A. (10, 8)**
### Step 1: Analyze the shape LMNPQR
The vertices of LMNPQR are:
- L(18,20)
- M(18,18)
- N(20,18)
- P(20,16)
- Q(16,16)
- R(16,20)
Here, we can observe the following:
- The shape consists of squares.
- It can be identified as a combination of squares connected to one another.
### Step 2: Find the dimensions and positioning
Since the shape LMNPQR is comprised of squares, we can analyze its dimensions:
- The vertical sides of the shape LMNPQR span from (16, 16) to (20, 20) and go down to (20, 16).
- The horizontal span is from (18, 18) to (20, 20).
The figure has a complex layout made from squares positioned in such a way that the overall 'L' shape is identifiable.
### Step 3: Analyze STUVWX
For figure STUVWX, we have:
- V(14, 4)
- W(6, 4)
- X(6, 12)
It can be observed that this shape has a vertical segment (from W to X) and a horizontal segment (from V to W).
### Step 4: Determine the right position for T
To find point T, we need to establish a criteria of similarity to LMNPQR. Since V and W are aligned horizontally and T needs to correspond to the proper 'closure' of the shape STUVWX.
There are two key principles here:
1. The shape must maintain the same proportionality as LMNPQR.
2. The corresponding point must fit into the angle created by V, W, and X.
Since we can deduce W is at (6, 4) and moves vertically to X at (6, 12), we must find T such that it closes the shape horizontally and connects in line with V or W.
Options for T position:
- A. (10, 8)
- B. (8, 8)
- C. (10, 10)
- D. (12, 8)
### Step 5: Evaluate options geometrically
- (10, 8): This point falls into a horizontal line between vertical coordinates of 4 and 12. It produces a clear "L" similar to LMNPQR.
- (8, 8): This point is slightly lower, but the structure would still be in alignment, though a little altered.
- (10, 10): This point sits too high vertically compared to the horizontal line that W at (6, 4) makes with V and results in disproportionality.
- (12, 8): This point results in elongated proportions preventing a suitable similarity ratio.
### Conclusion
The best option for T, closing figure STUVWX while ensuring that the resulting shape maintains a similarity to LMNPQR is:
**A. (10, 8)**