The perpendicular equation is y = -3/2x - 4.
You can find this by first realizing that perpendicular lines have opposite and reciprocal slopes. So since it starts at 2/3 we flip it and make it a negative and the new slope is -3/2. Now we can use that and the point to get the y intercept using slope intercept form.
y = mx + b
5 = (-3/2)(-6) + b
5 = 9 + b
-4 = b
And now we can use our new slope and new intercept to model the equation.
y = -3/2x - 4
Answer:
[(x+5)²+(y+3)²]
Step-by-step explanation:
- length = 5 units and width = 3 units
- x is for length as y is for width
- (x+5) for length & (y+3) for width
- [(x+5)²+(y+3)²]
F(x)=|x| is the simplified version of an absolute function such as the parent function
<h3>
Answer: Point T is at the location (4, 3)</h3>
================================================
Work Shown:
Let T be the point (x,y)
Point S is defined to be at (2,7)
The x coordinates of S and T are 2 and x in that order. Add them up and divide by 2 to get (2+x)/2. Set this equal to 3 as this is the x coordinate of the midpoint. We have this equation
(2+x)/2 = 3
Now solve for x
(2+x)/2 = 3
2+x = 2*3 .... multiply both sides by 2
2+x = 6
x = 6-2 .... subtract 2 from both sides
x = 4
-----------------
We'll follow similar logic and steps for the y coordinate of point T
S = (2,7)
T = (x,y)
The y coordinates for S and T are 7 and y in that order.
Add them up, divide by 2, then set the result equal to 5 (which is the y coordinate of the midpoint). Then solve for y.
(7+y)/2 = 5
7+y = 2*5 ..... multiply both sides by 2
y+7 = 10
y = 10-7 ..... subtract 7 from both sides
y = 3
----------------
Point T gets updated from (x,y) to (4, 3)
