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3 years ago

HELP A line passes through two points with coordinates (6,-8) and (-3,7).

Mathematics

1 answer:

FromTheMoon [43]3 years ago

4 0

Answer:

3y+5x=6

Step-by-step explanation:

Equation of the Line

The equation of a line passing through points (x1,y1) and (x2,y2) can be found as follows:

$\displaystyle y-y_1=\frac{y_2-y_1}{x_2-x_1}(x-x_1)$

The line passes through the points (6,-8) and (-3,7), thus:

$\displaystyle y+8=\frac{7+8}{-3-6}(x-6)$

$\displaystyle y+8=\frac{15}{-9}(x-6)$

Simplifying:

$\displaystyle y+8=-\frac{5}{3}(x-6)$

Multiplying by 3:

$3(y+8)=-5(x-6)$

$3y+24=-5x+30$

Moving all the variables to the left side:

3y + 5x = 30 - 24

3y + 5x = 6

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 Question #15

Step-by-step explanation:

A notation such as $T_{(-1, 1)}oR_{y-axis}$ is read as:

"a translation of (x, y) → (x - 1, y + 1) after a reflection across y-axis.

This process must be done from right to left
Composition of transformations is not commutative

The rule of reflection of point (x, y) across y-axis brings (x, y) → (-x, y), meaning that y-coordinate remains the same, but x-coordinate changes its sign.

As ΔABC with coordinates A(1, 3), B(4, 5) and C(5, 2). Here is the coordinates of ΔA'B'C' after the glide reflection described by $T_{(-1, 1)}oR_{y-axis}$ .

$R_{y-axis}$ $T_{(-1, 1)}$

A(1, 3) → A'(-1, 3) → A"'(-2, 4)

B(4, 5) → B'(-4, 5) → B"'(-5, 6)

C(5, 2) → C'(-5, 2) → C"'(-6, 3)

 Question #16

Step-by-step explanation:

A glide reflection is said to be a transformation that involves a translation followed by a reflection in which every point P is mapped to a point P ″ by the following steps.

First, a translation maps P to P′.
Then, a reflection in a line k parallel to the direction of the translation maps P′ to P ″.

As ΔABC with coordinates A(-4, -2), B(-2, 6) and C(4, 4).

Translation : (x, y) → (x + 2, y + 4)

Reflection : in the x-axis

The rule of reflection of point (x, y) across x-axis brings (x, y) → (x, -y), meaning that x-coordinate remains the same, but y-coordinate changes its sign.

Hence,

ΔABC with coordinates A(-4, -2), B(-2, 6), C(4, 4) after (x, y) → (x + 2, y + 4) and reflection in the x-axis.

A(-4, -2) → A'(-2, 2) → A''(-2, -2)

B(-2, 6) → B'(0, 10) → B''(0, -10)

C(4, 4) → C(6, 8) → C''(6, -8)

Keywords: reflection, glide reflection, translation

Learn more reflection, glide reflection, and translation from brainly.com/question/11570967

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