Question

the point p(2,9)and(a,5)and(5,5)or the verticies of a triangle PQRright angle at Q.find the value of A and hence the arc of triangle PQR

Answer 1

P (2, 9)    Q ( a, 5)  R (5, 5)
PQR is a right angle triangle. Q= 90 deg.  So  PQ is perpendicular to QR.

slope of PQ * slope of QR = -1
slope of QR = 0  => slope of QP  is infinity.  Hence  (9-5)/(2-a) = infinity.
a = 2.

you see that QR is parallel to x axis.  PQ is perpendicular t o  x axis.

base =  QR =3
height = PQ = 4

area =  1/2 * 3 * 4 = 6

Area =