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Solving 7th-grade math on page 70 of the workbook 'Creative Horizon' Volume 2 is a valuable resource to help students refer to detailed solutions for exercises 1, 2, 3, 4, 5, 6 of the topic 'Midpoint of a Line Segment' in the textbook. This enables students to grasp the knowledge and progressively excel in the subject of Mathematics.
Other excellent 7th-grade math resources:
- Solving 7th-grade math 'Creative Horizon'
- Solving 7th-grade math on page 84 of the workbook 'Connect the Knowledge' - Exercise 16: Isosceles Triangle. Midpoint of a Line Segment
- Solving 7th-grade math on page 103 of the workbook 'Kite' - Exercise 9. Midpoint of a Line Segment
Solving 7th-grade math on page 70 of the textbook 'Creative Horizon' Volume 2
Midpoint of a Line Segment
1. Solve Exercise 1 Page 70 Mathematics Grade 7 Textbook
Problem: Figure 10 illustrates a sheet of paper with the perpendicular bisector xy of line segment AB, where the image of point B is blurred. Describe how to determine point B.
Solution:
The line perpendicular to a line segment at its midpoint is called the perpendicular bisector of that segment.
Answer:
Let C be the intersection point of the line xy and the line segment AB.
Since xy is the perpendicular bisector of line segment AB, C is the midpoint of line segment AB.
Therefore, AC equals BC.
To determine point B, measure the length of line segment AC. On the opposite ray of ray CA, mark point B such that AC equals BC.
2. Solve Exercise 2 Page 70 Mathematics Grade 7 Textbook
Problem: Observe Figure 11, where M is the midpoint of BC, AM is perpendicular to BC, and AB equals 10 cm. Calculate AC.
Solution:
A point lying on the perpendicular bisector of a line segment is equidistant from both ends of that segment.
Answer:
Since M is the midpoint of line segment AB, and AM is perpendicular to BC, AM is the perpendicular bisector of line segment AB.
Therefore, AB equals AC. Given that AB equals 10 cm.
So, AC equals 10 cm.
3. Solve Exercise 3 Page 70 Mathematics Grade 7 Textbook
Problem: Observe Figure 12, where AM is the perpendicular bisector of line segment BC, and DB equals DC equals 8 cm. Prove that the points A, M, D are collinear.
Solution:
A point equidistant from both ends of a line segment lies on the perpendicular bisector of that segment.
Answer:
Since DB equals DC equals 8 cm, point D is equidistant from both ends of line segment BC.
Therefore, point B lies on the perpendicular bisector of line segment BC.
Consequently, the points A, M, D are collinear.
4. Solve Exercise 4 Page 70 Mathematics Grade 7 Textbook
Problem: Observe Figure 13, where AB equals AC and DB equals DC. Prove that M is the midpoint of BC.
Solution:
+ A point equidistant from both ends of a line segment lies on the perpendicular bisector of that segment.
+ A line perpendicular to a line segment at its midpoint is called the perpendicular bisector of that segment.
Answer:
Since AB equals AC and DB equals DC, points A and D are equidistant from both ends of line segment BC. Therefore, AD is the perpendicular bisector of line segment BC.
Since M is the intersection of AD and BC, M is the midpoint of line segment BC.
5. Solve Exercise 5 Page 70 Mathematics Grade 7 Textbook
Solution:
Solution:
A point on the perpendicular bisector of a line segment is equidistant from both ends of that segment.
Answer:
6. Solve Exercise 6 Page 70 Mathematics Grade 7 Textbook
Problem: On the urban planning map of a residential area, there is a road 'd' and two residential points A and B (shown below). Find a location M along the road to build a medical station so that it is equidistant from both residential points.
Solution:
A point on the perpendicular bisector of a line segment is equidistant from both ends of that segment.
Answer:
Let M be the location to build the medical station. Since M is equidistant from both residential points A and B, M lies on the perpendicular bisector of line segment AB. Additionally, point M lies on the road 'd'.
Therefore, M is the intersection of the line 'd' with the perpendicular bisector of line segment AB.
Here is the guide to solving 7th-grade math on page 70 workbook Volume 2. Students can also refer to the solutions on page 72 and review the exercises on page 66 for a solid understanding.
- Solve 7th-grade math on page 72 workbook 'Creative Horizon' Volume 2 - Exercise 6: Properties of three perpendicular bisectors of a triangle
- Solve 7th-grade math on page 66 workbook 'Creative Horizon' Volume 2 - Exercise 4: Perpendicular lines and diagonals
