(a) Construct a quadrilateral ABCD in which AB = 10cm , angle ABC = 120° , angle BAD = 60°, BC =7cm and AD = 11cm.

(b) Measure and write the length of CD.
(c) Within the quadrilateral ABCD draw the locus of points which are
(i) 8cm from A,
(ii) equidistant from BC and CD
(d) A point p , within the quadrilateral ABCD , is such that it is 8cm from A and equidistant from BC and CD .Label point p.
(e) Another point Q within the quadrilateral ABCD , is such that it is nearer to CD than to BC and greater than or equal to 8cm from A . indicate , by shading , the region in which Q must lie.

Ok, I made a sketch of your figure, we could not possible help you with your own.

I just followed the steps in sequence, was pretty straight-forward

b) can't help you with that, can't see your quad, but I could calculate it
(using the cosine law you can find CA, then by the sine law you can find angle CAB
after than find angle CAD, then by another cosine law you can find CD) , Did you get appr 8.7 ?

c) i) wouldn't that just be a circle with radius of 8 ?
ii) how about the bisector of angle BCD ?

d) mmmhhhh, how do you think that ties in with c) ?

e) go for it, you got your diagram.

That explanation doesn't help.

Show it then

(a) To construct the quadrilateral ABCD with the given specifications, follow these steps:

Step 1: Draw a line segment AB of length 10cm.
Step 2: At point B, construct an angle of 120 degrees.
Step 3: Measure a distance of 7cm along the ray of the angle to point C and mark it.
Step 4: At point A, construct an angle of 60 degrees.
Step 5: Measure a distance of 11cm along the ray of the angle to point D and mark it.
Step 6: Connect points C and D to complete the quadrilateral ABCD.

(b) To measure the length of CD, use a ruler or a measuring tape to measure the distance between the points C and D. The measured distance will be the length of CD.

(c) (i) To draw the locus of points that are 8cm from point A, follow these steps:

Step 1: From point A, use a compass to mark two points, one on each side of point A, at a distance of 8cm.
Step 2: Draw arcs with these marked points as centers to intersect the existing sides of quadrilateral ABCD.
Step 3: The locus of these intersection points will form the desired locus of points that are 8cm from point A.

(ii) To draw the locus of points equidistant from BC and CD, follow these steps:

Step 1: Using a compass, measure the distance between point B and the line segment CD.
Step 2: From point C, construct arcs on both sides of CD with the measured distance from step 1 as the radius.
Step 3: Repeat the process from point D, constructing arcs on both sides of CD with the same radius.
Step 4: The locus of points where the arcs intersect will be the desired locus of points equidistant from BC and CD.

(d) To label the point P, which is 8cm from A and equidistant from BC and CD, locate the intersection point of the two loci generated in step (c) (i) and (ii). Label this point as P.

(e) To indicate the region where point Q must lie, follow these steps:

Step 1: From point C, set your compass at a distance greater than the distance between CD and BC.
Step 2: Draw an arc that intersects BC within the quadrilateral ABCD.
Step 3: From point D, set your compass at a distance less than the distance between CD and BC.
Step 4: Draw an arc that intersects CD within the quadrilateral ABCD.
Step 5: Shade the region between the arcs drawn in steps 2 and 4. This shaded region represents the area where point Q can be located, which is closer to CD than to BC and at least 8cm from point A.