In the figure shown, the length of WX is 2 and the length of WY is 6. If point Z is the midpoint of XY, what is the length of WZ?
The length of WZ is 4.
To find the length of WZ, we first determine the coordinates of points W, X, and Y based on the given lengths. By placing W at the origin (0, 0), X at (2, 0), and Y at (2, 6), the midpoint Z of XY can be calculated as (2, 3). Using the distance formula, the length of WZ is found to be 4.
This option suggests that WZ is 2, which would imply that point Z is located closer to W than it actually is. Given the coordinates determined earlier, the distance from W to Z is clearly greater than 2, making this choice incorrect.
Choosing 3 for WZ would indicate that point Z is located slightly farther than the distance calculated. However, based on the coordinates established, the distance from W to Z is not 3, thus this choice is also incorrect.
This is the only correct choice. By calculating the distance from W (0, 0) to Z (2, 3) using the distance formula, we find that WZ equals 4, confirming this choice as accurate.
Selecting 8 suggests that Z is much further from W than the calculated distance. The coordinates clearly show that WZ cannot be 8, as this would require Z to be positioned significantly away from W, which is not supported by the given information.
The calculation of the distance from point W to the midpoint Z of segment XY reveals that WZ measures exactly 4 units. This conclusion is supported by the coordinates derived from the lengths of WX and WY, confirming option C as the only accurate measurement of distance in this context.
Related Questions
View allA circular garden is inscribed in a square lot of side length 6 meters...
Comets are composed mainly of
In the xy-plane, parallelogram ABCD is to be reflected across the x-ax...
Mary has a coupon for 15% off at a department store. She wants to buy...
The graph shows the relationship between metabolic rate and running sp...
Related Quizzes
View allPraxis 5001 Test with Answers
Praxis 5002 Study Guide
5002 Praxis Practice Test
Reading & Language Arts Praxis 5002
Praxis 5002 Reading and Language Arts Exam
Praxis 5003 Exam with Outline
5003 Praxis Math Answers
Praxis 5003 Study Guide
Praxis Social Studies 5004
Praxis 5004 Social Studies
- ✓ 500+ Practice Questions
- ✓ Detailed Explanations
- ✓ Progress Analytics
- ✓ Exam Simulations