Segment is long

MATHEMATICS · Subjective · GCSE · Mathematics · Geometry and Measures · Geometry and Measures

Problem

Segment

XY

6\text{ cm}

long. Describe the locus of all points

Z

in the plane such that

\triangle XYZ

is congruent (with corresponding sides in the same order) to a triangle whose sides are

6\text{ cm}

5\text{ cm}

and

4\text{ cm}

. State also how many such points exist.