在此比例图中,A、B 和 C 是公园 ABCD 的三个角,其中 C 在 B 的正北方向。

- (a)
作 BC 的垂直平分线。
- (b)
D 位于 A 的方位角 065° 方向,且到 B 和 C 的距离相等。
在图上标出点 D。
- (c)
作角 ABC 的角平分线。
- (d)
埃莉诺站在公园 ABCD 内,使得她离 BC 的距离比离 AB 更近,且离 B 比离 C 更近。
阴影表示埃莉诺可能站立的区域。
它不会直接告诉你答案,而是问你卡在哪一步看看 AI 是怎么陪你一步步弄懂这道题的
完整解法
22(a)
1. Construct the perpendicular bisector of $BC$ accurately.
Set the compass radius to more than half of . With centre , draw arcs on both sides of . Using the same radius with centre , draw arcs to intersect the first pair of arcs. Join the two arc intersection points with a straight line.
This line is the perpendicular bisector of .
The perpendicular bisector of is constructed: a straight line crossing at and passing through the midpoint of .
22(b)
1. Draw the locus satisfying the bearing condition from $A$.
From , draw a north line. Measure a clockwise angle of from north and draw the ray from on this bearing.
2. Use the equidistant condition to locate and label $D$.
Since is equidistant from and , lies on the perpendicular bisector of constructed in part (a). Mark the intersection of the bearing ray from with this perpendicular bisector and label it .
Point is marked and labelled at the intersection of the bearing line from and the perpendicular bisector of .
22(c)
1. Construct the angle bisector of $\angle ABC$ accurately.
Using a compass, draw an arc centred at to cut and . From the two intersection points, draw equal-radius arcs to meet inside . Draw a straight line from through the intersection of these arcs. This line is the bisector of .
The bisector of angle is constructed: a straight line/ray from that divides into two equal angles.
22(d)
1. Identify the two locus boundaries and choose the correct side of each boundary.
Points closer to line than to line lie on the side of the angle bisector of .
Points closer to than to lie on the side of the perpendicular bisector of .
Therefore, shade the intersection of these two half-regions inside the park .
Shade the region inside that is on the side of the angle bisector of and on the side of the perpendicular bisector of .
AI 分析,可能出错
用 AI 批改,圈出写错的那一步,并自动将你的薄弱点存入错题本,形成你的错因库。
同一知识点的其他题
- 1在比例图中,PQRS 代表一片用于建公园的土地。 比例尺:1 cm 代表 0.5 km 求 P 与 Q 之间的实际距离。 答:___ km 测量从 S 观测 P 的方位角。 答:___ ° 作 ∠PQR 的角平分线。 作 RS 的垂直平分线…
- 2图中显示了一条线段 PQ。 尺规作图画出 PQ 的垂直平分线,并清晰地保留作图痕迹。 答案 清晰地解释为什么你的作图方法能够得到 PQ 的垂直平分线。 答案 ___
- 3图中显示了一个四边形 PQRS。 作 SR 的垂直平分线,使其与 PQ 相交于点 Z。 标出并注明点 Z。 测量并写出角 PZS 的大小。 答:...°
- 4已知三个点,,,则的外心的纵坐标是 A. B. C. …
- 5在联欢晚会上,有、、三名同学站在一个三角形的三个顶点位置上,他们在玩抢凳子游戏,要求在他们中间放一个木凳,谁先抢到凳子谁获胜,为使游戏公平,则凳子应放的最适当的位置在的( )…