Question

coordinate plane
key concept • locating a point at fractional distances on a number line
find the coordinate of a point that is \\(\frac{a}{b}\\) of the distance from point c
to point d.
step 1 calculate the difference
of the coordinates of
point c and point d.
\\((x_2 - x_1)\\) with number line chart: c at (x_1), d at (x_2)
step 2 multiply the difference
by the given fraction.
the fractional distance is
given by \\(\frac{a}{b}(x_2 - x_1)\\). with number line chart: c at (x_1), d at (x_2), fractional distance marked
step 3 add the fractional
distance to the
coordinate of the
initial point (x_1).
the coordinate of point p is
given by \\(x_1 + \frac{a}{b}(x_2 - x_1)\\). with number line chart: c at (x_1), p, d at (x_2)
find x on \\(\overline{be}\\) that is \\(\frac{3}{5}\\) of the distance from b to e.
number line: b at -1, e at 9, marked from -5 to 10: -5 -4 -3 -2 -1 0 1 2 3 4 5 6 7 8 9 10

Explanation:

Step1: Identify coordinates of B and E

From the number line, coordinate of \( B \) (\( x_1 \)) is \(-1\), coordinate of \( E \) (\( x_2 \)) is \( 9 \).

Step2: Calculate the difference \( x_2 - x_1 \)

\( x_2 - x_1 = 9 - (-1) = 9 + 1 = 10 \)

Step3: Multiply the difference by the fraction \( \frac{3}{5} \)

\( \frac{3}{5}(x_2 - x_1) = \frac{3}{5} \times 10 = 6 \)

Step4: Add the result to \( x_1 \)

Coordinate of \( X = x_1 + \frac{3}{5}(x_2 - x_1) = -1 + 6 = 5 \)

Answer:

The coordinate of point \( X \) is \( 5 \)