Geometrical Deductions

What is abductive reasoning? Given one example.

Define abductive reasoning.

A man transports a fox, a duck and corn in a boat. The boat is only capable of transporting himself and one of the other three with each crossing. How did he succeed in crossing them all without letting the fox eat the duck or the duck eat the corn?

Define logic and explain three types of logical reasoning.

The shortest distance from $P\left(5,6\right)$ to the line $2x+y=6$ is 

The shortest distance from $P\left(2,0\right)$ to the line $y=x+1$ is 

Plot the coordinates $(3, 5)$ and $(5, -4)$.

What Is Deductive Reasoning? Give examples.

What is the difference between inductive and deductive reasoning?

Find the figure from Answer Figures which will continue the series in question.

A line segment on the coordinate plane has endpoints $P\left(a-5,-b\right)$ and $Q\left(b+8,a-4\right)$. The midpoint of the line segment is $\left(2,3\right)$. Find the coordinates of $P$ and $Q$.

Find the sum of the squares of the sides of the triangle formed by $\mathrm{F}(-6,5),\mathrm{G}(-4,5),\text{ and }\mathrm{H}(-5,9)$.

$ABC$ is a triangle with vertices $A(1,0), B(5,9)\text{ and }C(9,0)$. The midpoints of the three sides of $ABC$ are the vertices of a/an _____ triangle.

The points$F(-6,5),G(-4,5),\text{ and }H(-5,9)$ form a/an _____ triangle.

Find the distance between pair of points: $(3,11)\text{ and }(6,15)$.

Given points are: $A(a,b)\text{ and }B(c,d)$. The point $\left(\frac{2a+c}{3},\frac{2b+d}{3}\right)$ divides the line segment $AB$ in the ratio $1:2$.

When archaeologists excavate a site, they mark it off with a coordinate grid so that they can easily identify where artefacts are found and keep a record of the site forever. At the West Kennet Long Barrow in England, a grave site dating back to $3600$ BCE, there are three chambers at the coordinates  $(7,9),(17,33),\text{ and }(-36,41)$. It has been said that they form an isosceles triangle. Determine whether the statement is true.

The points $A(2,5),B(4,19),C(14,29),\text{ and }D(12,15)$ form a rhombus. $E,F,G,\text{ and }H$ are the midpoints of $AB, BC, CD$ and $DA$ respectively. Name the shape $EFGH$.

The points $A(2,5),B(4,19),C(14,29),\text{ and }D(12,15)$ forms a

Find the midpoint of $A(14,-2)\text{ and }B(6,11)$.