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: Find the slope - formula

The slope formula between two points $(x_1,y_1)$ and $(x_2,y_2)$ is $m=\frac{y_2 - y_1}{x_2 - x_1}$. For points $A(2,4)$ and $B(10,6)$, $m=\frac{6 - 4}{10 - 2}=\frac{2}{8}=\frac{1}{4}$.

Step2: Find the distance between points in x - direction

The difference in x - coordinates between $A$ and $B$ is $\Delta x=10 - 2 = 8$. If $\overline{AB}$ is divided into 8 equal parts, the increment in x - coordinate for each part is 1.

Step3: Find the increment in y - coordinate

Since the slope $m=\frac{1}{4}$, for an increment of 1 in the x - coordinate, the increment in the y - coordinate is $\frac{1}{4}=0.25$.

Step4: Calculate coordinates of points

For point $D$: Starting from $A(2,4)$, if we move 2 units in the x - direction (because for $D$ we are 2 parts away from $A$), the x - coordinate is $2+2 = 4$, and the y - coordinate is $4+2\times0.25=4 + 0.5=4.5$. So $D=(4,4.5)$.
For point $E$: Moving 3 units in the x - direction from $A$, the x - coordinate is $2 + 3=5$, and the y - coordinate is $4+3\times0.25=4 + 0.75 = 4.75$. So $E=(5,4.75)$.
For point $H$: Moving 7 units in the x - direction from $A$, the x - coordinate is $2+7 = 9$, and the y - coordinate is $4+7\times0.25=4 + 1.75=5.75$. So $H=(9,5.75)$.
For point $I$: Moving 6 units in the x - direction from $A$, the x - coordinate is $2+6 = 8$, and the y - coordinate is $4+6\times0.25=4 + 1.5=5.5$. So $I=(8,5.5)$.

Answer:

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