Question

bookwork code: 1e calculator not allowed mark the points a and b in your book 4 cm apart. construct and shade the region that is closer to b than to a and within 3 cm of b. you must show all of your construction lines. a·

Explanation:

Step1: Locate Point B

Measure 4 cm from point A (using a ruler) and mark point B, so \( AB = 4 \, \text{cm} \).

Step2: Draw Perpendicular Bisector (for "closer to B than A")

Find the midpoint of \( AB \) (since the set of points equidistant from A and B is the perpendicular bisector of \( AB \)). The midpoint \( M \) divides \( AB \) into two equal parts (\( AM = MB = 2 \, \text{cm} \)). Draw the perpendicular bisector of \( AB \) (using a compass: set compass width > 2 cm, draw arcs from A and B, connect intersection points). Points closer to B lie on the B - side of this bisector.

Step3: Draw Circle Centered at B (for "within 3 cm of B")

Set a compass to 3 cm. Place the compass tip at B and draw a circle (all points on this circle are 3 cm from B, and inside are within 3 cm).

Step4: Identify the Region

The desired region is the area that is inside the circle centered at B (radius 3 cm) and on the B - side of the perpendicular bisector of \( AB \). Shade this overlapping region, showing all construction lines (perpendicular bisector, circle, and segment \( AB \)).

Answer:

The region is the intersection of the interior of the circle (center \( B \), radius \( 3 \, \text{cm} \)) and the half - plane on the \( B \) - side of the perpendicular bisector of \( AB \). Construction lines include \( AB \), the perpendicular bisector of \( AB \), and the circle centered at \( B \) with radius \( 3 \, \text{cm} \), with the overlapping region shaded.