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2 years ago

13

Write the equation in point-slope form of the line that passes

1 answer:

mariarad [96]2 years ago

3 0

Answer:

y + 2 = 5/3(x - 4)

Step-by-step explanation:

Point-slope form of the equation of a line is a shortcut, fill-in-the-blank formula. You can write an equation just by filling in the slope and a point (hence the name, point-slope)

It looks like this:

y - Y = m(x - X)

The point given is (4,-2) fill in the -2 for the Y. Leave the first y just like it is, it stays a y. Fill in the 4 for X. Leave the first little x in the parenthesis alone Leave it an x.

y - -2 = m(x - 4)

Fill in the slope for the m.

y - -2 = 5/3(x - 4)

Simplify if possible.

y + 2 = 5/3 (x - 4)

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Answer:

Part A) The area of the figure is $24\ units^{2}$

Part B) The perimeter of the figure is $20\ units$

Step-by-step explanation:

step 1

Find the area of the figure

we know that

The area of the figure is equal to the area of triangle ABD plus the area of triangle BCD

The area of triangle is equal to

$A=\frac{1}{2}bh$

<u>Area of triangle ABD</u>

Observing the graph

$b=BD=(-2+8)=6\ units$

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substitute

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<u>Area of triangle BCD</u>

Observing the graph

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substitute

$A=\frac{1}{2}(6)(4)=12\ units^{2}$

The area of the figure is

$12\ units^{2}+12\ units^{2}=24\ units^{2}$

step 2

Find the perimeter of the figure

we know that

The perimeter of the figure is equal to

$P=AB+BC+CD+AD$

we have

$A(-5,1),B(-8,5),C(-5,9),D(-2,5)$

the formula to calculate the distance between two points is equal to

$d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}$

Find the distance AB

$d=\sqrt{(5-1)^{2}+(-8+5)^{2}}=5\ units$

Find the distance BC

$d=\sqrt{(9-5)^{2}+(-5+8)^{2}}=5\ units$

Find the distance CD

$d=\sqrt{(5-9)^{2}+(-2+5)^{2}}=5\ units$

Find the distance AD

$d=\sqrt{(5-1)^{2}+(-2+5)^{2}}=5\ units$

substitute the values

$P=5+5+5+5=20\ units$

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