MATH SOLVE

3 months ago

Q:
# Find the point that is 1/5 the way from A to B whereA(-7,4) and B(3, 10).

Accepted Solution

A:

Answer:The coordinates of the point that is 1/5 the way from A to B is [tex](x,y) = (-5,\frac{26}{5})[/tex]Step-by-step explanation:Here, the given points are: A (-7,4) and B (3,10)Let us assume the point M(x,y) on AB is such that AM : AB = 1 : 5⇒ AM : (AB - AM) = 1 : (5-1) = 1: 4⇒ AM : MB = 1 : 4Now, The Section Formula states the coordinates of point (x,y) on any line dividing the line in the ratio m1 : m2[tex](x,y) = (\frac{m_2x_1+m_1x_2}{m_1+m_2} ,\frac{m_2y_1+m_1y_2}{m_1+m_2} )[/tex]Here, in the given equation, m1: m2 = 1:4So, the coordinates M(x,y) is given as:[tex](x,y) = (\frac{(-7)(4) + 1 (3)}{1+ 4} ,\frac{4(4) + 1(10)}{1+4} )\\\implies (x,y) = (\frac{-28+3}{5} ,\frac{16+10}{5} ) = (\frac{-25}{5} ,\frac{26}{5} )\\\implies (x,y) = (-5,\frac{26}{5} )[/tex]Hence, the coordinates of the point that is 1/5 the way from A to B is [tex](x,y) = (-5,\frac{26}{5})[/tex]