Which two-dimensional figure could be a cross section of a rectangular pyramid that has been intersected by a plane perpendicula
1 answer:
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The equation in slope intercept form of a line that is a perpendicular bisector of segment AB with endpoints A(-5,5) and B(3,-3) is y = x + 2
<h3><u>Solution:</u></h3>Given, two points are A(-5, 5) and B(3, -3)
We have to find the perpendicular bisector of segment AB.
Now, we know that perpendicular bisector passes through the midpoint of segment.
<em><u>The formula for midpoint is:</u></em>
<em><u>Finding slope of AB:</u></em>
We know that product of slopes of perpendicular lines = -1
So, slope of AB slope of perpendicular bisector = -1
- 1 slope of perpendicular bisector = -1
Slope of perpendicular bisector = 1
We know its slope is 1 and it goes through the midpoint (-1, 1)
<em><u>The slope intercept form is given as:</u></em>
y = mx + c
where "m" is the slope of the line and "c" is the y-intercept
Plug in "m" = 1
y = x + c ---- eqn 1
We can use the coordinates of the midpoint (-1, 1) in this equation to solve for "c" in eqn 1
1 = -1 + c
c = 2
Now substitute c = 2 in eqn 1
y = x + 2
Thus y = x + 2 is the required equation in slope intercept form
Answer:
(12,10)
Step-by-step explanation:
Let the midpoint of the side opposite this vertex have coordinates B(a,b)
We have the centroid at C(8,7) and the vertex of the triangle at A(0,1).
The centroid divides AB internally in the ratio 2:1
We use the formula:
where m:n=2:1 is the ratio of internal division.
We substitute the coordinates of A and B and the ratio to get:
This should simplify and give us the centroid.
This implies that:
We solve for a and b
Therefore the midpoint of the side opposite this vertex is (12,10)