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4 years ago

PLEASEEEE ANSWERRR FASTTTT!!!!!!!!!!What is the equation of the line whose graph is shown?

Mathematics

1 answer:

Mamont248 [21]4 years ago

8 0

Answer:

Step-by-step explanation:

The equation of a line passing through the origin is

y = mx ( m is the slope )

To find m use the slope formula

m = ( y₂ - y₁ ) / ( x₂ - x₁ )

with (x₁, y₁ ) = (1, 1) and (x₂, y₂ ) = (- 1, - 1) ← 2 points on the line

m = $\frac{-1-1}{-1-1}$ = $\frac{-2}{-2}$ = 1

y = x ← is the equation of the line → A

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Answer:

y = 8

Step-by-step explanation:

Two triangles are said to be congruent if all the three sides and three angles of both triangles are equal.

The distance between two points on the coordinate plane is given as:

$Distance=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2} \\$

In triangle ABC:

$|AB|=\sqrt{(2-8)^2+(6-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|AC|=\sqrt{(5-8)^2+(0-4)^2}=5\\\\|BC|=\sqrt{(5-2)^2+(0-6)^2 }=\sqrt{45}$

In triangle MNO:

$|MN|=\sqrt{(1-7)^2+(2-4^2)}=\sqrt{40} =2\sqrt{10}\\\\|MO|=\sqrt{(4-7)^2+(y-4)^2}\\\\|NO|=\sqrt{(4-1)^2+(y-2)^2 }$

Since triangle ABC and triangle MNO are congruent, hence:

|AB| = |MN| = 2√10, |AC| = |MO| = 5, |BC| = |NO| = √45

$|AC|=|MO|=5\\\\\sqrt{(4-7)^2+(y-4)^2}=5\\\\(4-7)^2+(y-4)^2=25\\\\9 +(y-4)^2=25\\\\(y-4)^2=16\\\\square\ root\ of\ both\ sides:\\\\y-4=4\\\\y=4+4\\\\y=8$

Hence O = (4, 8)

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