Question

Find the point that is one-fourth of the way from P(1,8) to Q(-7,8)

Answer 1

Given two points P(–1, 3) and Q(7, 5)

➊ METHOD ONE

Let M name the midpoint between P and Q

M has co-ords ( ½(Xp +Xq), ½(Yp + Yq) )

= ( ½(–1 + 7), ½(3 + 5) )

= ( ½(6), ½(8) )

= (3, 4)

Let N name the mid point between P and M.

N will have co-ords: ( ½(Xp +Xm), ½(Yp + Ym) )

= ( ½(–1 + 3), ½(3 + 4) )

= ( ½(2), ½(7) )

= (1, 3½)


➋ METHOD TWO (which is more efficient ie gets an answer more quickly)

Let N name the point that is "one-fourth of the distance from the point P to the point Q along the segment PQ"

N will have co-ords: (Xp + ¼(Xq – Xp), Yp + ¼(Yq – Yp)

This means that Xn is Xp + one quarter of the difference between Xq and Xp
This means that Yn is Yp + one quarter of the difference between Yq and Yp

= (–1 + ¼(7 – (–1)), 3 + ¼(5 – 3) )

= (–1 + ¼(8), 3 + ¼(2) )

= (–1 + 2, 3 + ½ )

= (1, 3½)


Hope this helps! God Bless You :)

Answer 2

Awesome! Thank you so much!

Answer 3

Np:)