Question

Point T partitions segment JZ at a ratio of 1:2 from point J. If point Z is located at (2,2) and point T is located at (4,-2) , where is point J located?​

Answer 1

The location of point J is at (8, -10) if point Z is located at (2,2) and point T is located at (4,-2),

The midpoint theorem is expressed as:

$M(x, y)=(\frac{ax_1+bx_2}{a+b} \frac{ay_1+by_2}{a+b} )$

where:

a:b be in the ratio of 1:2

Substitute the given coordinates T(4, -2) and Z(2, 2) into the formula to get the coordinate J(x₁, y₁)

$x =\frac{ax_1+bx_2}{a+b}\\4 =\frac{1x_1+2(2)}{1+2}\\4(3) = x_1+4\\12 = x_1 + 4\\x_1 = 8$

Get the other coordinate of J, y1

$y =\frac{ay_1+by_2}{a+b}\\-2 =\frac{1y_1+2(2)}{1+2}\\-2(3) = y_1+4\\-6 = y_1 + 4\\y_1 = -6-4\\y_1 =-10$

Hence the location of point J is at (8, -10) if point Z is located at (2,2) and point T is located at (4,-2).

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