## IGCSE Mathematics 0580/04/SP/20 Q6

Question

*6*

*OPQR *is a rectangle and *O *is the origin.

*M *is the midpoint of *RQ *and *PT *: *TQ *= 2 : 1.

*OP *=** P **and *OR *= **r.**

**(a) **Find, in terms of** p **and/or **r**, in its simplest form

**(i) ***MQ*,

**(ii) ***MT *,

**(iii) ***OT *.

*(b) **RQ *and *OT *are extended and meet at *U*.

Find the position vector of *U *in terms of **p** and **r**.

Give your answer in its simplest form.

**(c)** *MT *= −(2*k/*-k) and *MT *= 180.

Find the positive value of *k*.

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