Question

compiled by: nyamasoka hardwork (b) measure and write down the length of bc. 1 (c) construct the locus of a point (i) that is 4,5 cm from b, (ii) x, on the same side of ad as c, such that the area of triangle acd = area of triangle axd. 3 (d) mark and label x1 and x2, the points that are 4,5 cm from b and are such that the area of triangle ax1d = the area of triangle ax2d. 2

Explanation:

Step1: Measure BC

Use a ruler to measure the length of line - segment BC in the given figure.

Step2: Construct locus of points 4.5 cm from B

Using a compass, with center at B and radius 4.5 cm, draw a circle. This circle is the locus of points that are 4.5 cm from B.

Step3: Construct locus for equal - area triangles

Since the area of $\triangle ACD=\triangle AXD$, and triangles with the same base (AD) have equal areas when they have the same height. So, the locus of point X is a line parallel to AD on the same side of AD as C.

Step4: Mark points $X_1$ and $X_2$

The intersection points of the circle (locus of points 4.5 cm from B) and the line parallel to AD (locus for equal - area triangles) are the points $X_1$ and $X_2$.

Answer:

(b) The length of BC is obtained by measurement with a ruler.
(c)(i) A circle with center B and radius 4.5 cm. (ii) A line parallel to AD on the same side of AD as C.
(d) The intersection points of the circle and the parallel line are marked as $X_1$ and $X_2$.