Question

What are the coordinates of the point 3/4 of the way from X(1, -6) to Y(9, 10)?

Answer 1

Answer:

$P(x,y) = (7,6)$

Step-by-step explanation:

Given

$X = (1,-6)$

$Y = (9,10)$

$Point = \frac{3}{4}$

Required

Determine the coordinate of the point;

First, we need to determine the ratio of the point between X and Y

Represent the point with P

If the distance between point X and point P is $\frac{3}{4}$,

The distance between point P and point Y will be $1 - \frac{3}{4} = \frac{1}{4}$

$Ratio = XP : PY$

$Ratio = \frac{3}{4} : \frac{1}{4}$

Multiply through by 4

$Ratio = 3: 1$

Now, the coordinate of P can be calculated using

$P(x,y) = (\frac{mx_2 + nx_1}{n+m},\frac{my_2 + ny_1}{n+m})$

Where

$m:n = 3:1$

$(x_1,y_1) = (1,-6)$

$(x_2,y_2) = (9,10)$

Substitute these values in the formula above

$P(x,y) = (\frac{3 * 9 + 1 * 1}{3+1},\frac{3 * 10 + 1 * -6}{3+1})$

$P(x,y) = (\frac{27 + 1}{4},\frac{30 -6}{4})$

$P(x,y) = (\frac{28}{4},\frac{24}{4})$

$P(x,y) = (7,6)$