Question

drag the tiles to the boxes to form correct pairs. not all tiles will be used.

in the figure, $overline{ab}$ is divided into equal parts. the coordinates of point a are (2, 4), and the coordinates of point b are (10, 6). match each pair of coordinates to the corresponding point on $overline{ab}$.

(4, 4.5) d (4, 4.75) e (9, 5.75) h (8, 5.75)
i (8, 5.5) (5, 4.75) (7, 5.25)

Explanation:

Step1: Count total equal segments

Count the intervals between A and B: there are 16 equal segments.

Step2: Calculate x-increment per segment

Total x-change: $10 - 2 = 8$. Increment per segment: $\frac{8}{16} = 0.5$

Step3: Calculate y-increment per segment

Total y-change: $6 - 4 = 2$. Increment per segment: $\frac{2}{16} = 0.125$

Step4: Find coordinates for D (4th segment)

A is (2,4). D is 4 segments from A:
$x = 2 + 4\times0.5 = 4$, $y = 4 + 4\times0.125 = 4.5$

Step5: Find coordinates for E (6th segment)

E is 6 segments from A:
$x = 2 + 6\times0.5 = 5$, $y = 4 + 6\times0.125 = 4.75$

Step6: Find coordinates for H (12th segment)

H is 12 segments from A:
$x = 2 + 12\times0.5 = 8$, $y = 4 + 12\times0.125 = 5.5$

Step7: Find coordinates for I (14th segment)

I is 14 segments from A:
$x = 2 + 14\times0.5 = 9$, $y = 4 + 14\times0.125 = 5.75$

Answer:

$D \longleftrightarrow (4, 4.5)$
$E \longleftrightarrow (5, 4.75)$
$H \longleftrightarrow (8, 5.5)$
$I \longleftrightarrow (9, 5.75)$