b> Find the equation to the straight lines passing through (1,1) and parallel to the lines represented by x²-5xy+4y²+x+2y-2=0
1 answer:
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Answer:
Part 1)
Part 2)
Part 3)
Step-by-step explanation:
step 1
Find the measure of length side FG
In the right triangle EFG
we know that
----> by SOH (opposite side divided by the hypotenuse)
substitute the given values
step 2
Find the measure of length side EF
In the right triangle EFG
we know that
----> by CAH (adjacent side divided by the hypotenuse)
substitute the given values
step 3
Find the measure of angle G
we know that
---> by complementary angles in a right triangle
Answer:
D) y = -4/5x – 47/10
Step-by-step explanation:
Step 1. Find the <em>midpoint of the segmen</em>t.
The two end points are (-6, -4) and (-2, 1).
The midpoint is at the average of the coordinates.
(xₚ, yₚ) = ((x₁ + x₂)/2, (y₁ + y₂)/2)
(xₚ, yₚ) = ((-6 - 2)/2, (-4 + 1)/2)
(xₚ, yₚ) = (-8/2, -3/2)
(xₚ, yₚ) = (-4, -3/2)
===============
Step 2. Find the <em>slope (m₁) of the segment</em>
m₁ = (y₂ - y₁)/(x₂ - x₁)
m₁ = (1 - (-4))/(-2 - (-6))
m₁ = (1 + 4)/(-2 + 6)
m₁ = 5/4
===============
Step 3. Find the <em>slope (m₂) of the perpendicular bisector </em>
m₂ = -1/m₁
m₂ = -4/5
====================
Step 4. Find the <em>intercept of the perpendicular bisector</em>
y = mx + b
y = -(4/5)x + b
The line passes through (-4, -3/2).
-3/2 = -(4/5)(-4) + b
-3/2 = 16/5 + b Multiply each side by 10
-15 = 32 + 10 b Subtract 32 from each side
-47 = 10b Divide each side by 10
b = -47/10
===============
Step 5. Write the <em>equation for the perpendicular bisector</em>
y = -4/5x – 47/10
The graph shows the midpoint of your segment at (-4, -3/2) and the perpendicular bisector passing through the midpoint and (0, -47/10).
