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3 years ago

Find the equation lines (4, 5)(7, 3)

Mathematics

1 answer:

mash [69]3 years ago

8 0

Step-by-step explanation:

Hey there!

The equation of a st.line passing through points (4,5) and (7,3) is;

$(y - y1) = \frac{y2 - y1}{x2 - x1} (x - x1)$

Put all values.

$(y - 5) = \frac{3 - 5}{7 - 4} (x - 4)$

Simplify it.

$(y - 5) = \frac{ - 2}{3} (x - 4)$

$3(y - 5) = - 2x + 8$

$3y - 15 = - 2x + 8$

$2x + 3y - 23 = 0$

Therefore therequired equation is 2x+3y-23=0.

Hope it helps..

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2 years ago

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3 years ago

Which series of transformations will not map figure H onto itself

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Answer:

Step-by-step explanation:

Given a square with vertices at points (2,1), (1,2), (2,3) and (3,2).

Consider option A.

1st transformation $(x+0,y-2)$ will map vertices of the square into points

$(2,1)\rightarrow (2,-1);$
$(1,2)\rightarrow (1,0);$
$(2,3)\rightarrow (2,1);$
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2nd transformation = reflection over y = 1 has the rule (x,2-y). So,

$(2,-1)\rightarrow (2,3);$
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$(2,1)\rightarrow (2,1);$
$(3,0)\rightarrow (3,2)$

These points are exactly the vertices of the initial square.

Consider option B.

1st transformation $(x+2,y-0)$ will map vertices of the square into points

$(2,1)\rightarrow (4,1);$
$(1,2)\rightarrow (3,2);$
$(2,3)\rightarrow (4,3);$
$(3,2)\rightarrow (5,2).$

2nd transformation = reflection over x = 3 has the rule (6-x,y). So,

$(4,1)\rightarrow (2,1);$
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$(4,3)\rightarrow (2,3);$
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These points are exactly the vertices of the initial square.

Consider option C.

1st transformation $(x+3,y+3)$ will map vertices of the square into points

$(2,1)\rightarrow (5,4);$
$(1,2)\rightarrow (4,5);$
$(2,3)\rightarrow (5,6);$
$(3,2)\rightarrow (6,5).$

2nd transformation = reflection over y = -x + 7 will map vertices into points

$(5,4)\rightarrow (3,2);$
$(4,5)\rightarrow (2,3);$
$(5,6)\rightarrow (1,2);$
$(6,5)\rightarrow (2,1)$

These points are exactly the vertices of the initial square.

Consider option D.

1st transformation $(x-3,y-3)$ will map vertices of the square into points

$(2,1)\rightarrow (-1,-2);$
$(1,2)\rightarrow (-2,-1);$
$(2,3)\rightarrow (-1,0);$
$(3,2)\rightarrow (0,-1).$

2nd transformation = reflection over y = -x + 2 will map vertices into points

$(-1,-2)\rightarrow (4,3);$
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3 years ago

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