Q 28. Plot the points P(0,4) and Q(0,-4) on the graph paper. Now plot the points R and S so that triangle PQR and triangle PQS are isosceles triangles. How many isosceles triangles can be formed.

Dear Student,

First we consider points S(-3,0) and R(3,0) on x-axis now lets find out the length of PS.P is represented as 0,4 and S as -3,0Distance PS=-3-02+0-42                PS=9+16               PS=25                PS=5 unitSimilarly we can find out the length QS from point S-3,0 and Q(0,-4)SQ=0+32+-4-02SQ=9+16SQ=5unit  And ,QR from point Q(0,-4) and R(3,0)QR=3-02+0+42QR=9+16QR=5unitSimilarlyPR from point P(0,4) and R(3,0)PR=3-02+0-42PR=9+16PR=5unitSo, PR=QR=QS=PS =  unit

Hence from the graph we have  4 isosceles triangles

Hope this information will clear your doubts about topic.

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