Answer:
1. See attachment.
2. x = 7.4
3. PN = 46.6
4. PW = 93.2
Explanation:
Perpendicular bisector: A line that bisects (divides into two equal parts) the original line at 90°.
Question 1
- Place the point of the compass on point X and set it to any width more than the half of XY. Draw an arc either side of line segment XY.
- Do not change the width of the compass. Place the point of the compass on point Y. Draw two arcs that intercept the arcs you drew in step 1.
- Draw a straight line through the points of intersection of the pairs of arcs. This is the perpendicular bisector of XY.
Question 2
If g is the perpendicular bisector of PW then:
⇒ WN = PN
⇒ 9x - 20 = 4x + 17
⇒ 9x - 20 - 4x = 4x + 17 - 4x
⇒ 5x - 20 = 17
⇒ 5x - 20 + 20 = 17 + 20
⇒ 5x = 37
⇒ 5x ÷ 5 = 37 ÷ 5
⇒ x = 7.4
Question 3
To find the length of PN, substitute the found value of x into the expression for PN:
⇒ PN = 9x - 20
⇒ PN = 9(7.4) - 20
⇒ PN = 66.6 - 20
⇒ PN = 46.6
Question 4
As PN = WN then:
⇒ PW = 2PN
⇒ PW = 2 × 46.6
⇒ PW = 93.2