we know that
the formula to calculate the distance between two points is equal to
[tex]d=\sqrt{(y2-y1)^{2}+(x2-x1)^{2}}[/tex]
Step [tex]1[/tex]
Find the distance TU
[tex]T(80,20)[/tex]
[tex]U(20,60)[/tex]
substitute the values
[tex]d=\sqrt{(60-20)^{2}+(20-80)^{2}}[/tex]
[tex]d=\sqrt{(40)^{2}+(-60)^{2}}[/tex]
[tex]d=\sqrt{1,600+3,600}[/tex]
[tex]d=\sqrt{5,200}\ units[/tex]
[tex]dTU=72\ units[/tex]
Step [tex]2[/tex]
Find the distanceUV
[tex]U(20,60)[/tex]
[tex]V(110,85)[/tex]
substitute the values
[tex]d=\sqrt{(85-60)^{2}+(110-20)^{2}}[/tex]
[tex]d=\sqrt{(25)^{2}+(90)^{2}}[/tex]
[tex]d=\sqrt{625+8,100}[/tex]
[tex]d=\sqrt{8,725}\ units[/tex]
[tex]dUV=93\ units[/tex]
Step [tex]3[/tex]
Sum the distances TU and UV
[tex]72\ units+93\ units=165\ units[/tex]
therefore
the answer is
the option 165 units
shortest distance = 165 units
This will be solved using distance formula between two coordinates.
The distance formula between two coordinates is given as;
d = [tex]\sqrt{(y_{2} - y_{1})^{2} + (x_{2} - x_{1})^{2}}[/tex]
Point T has coordinate of T(80,20)
Distance to Point U(20,60) is;
TU = [tex]\sqrt{(60 - 20)^{2} + (20 - 80)^{2}}[/tex]
TU = [tex]\sqrt{5200}[/tex]
TU ≈ 72 Units
Distance From Point U(20,60) to Point V(110,85);
UV = [tex]\sqrt{(85 - 60)^{2} + (110 - 20)^{2}}[/tex]
UV = [tex]\sqrt{8725}[/tex]
UV ≈ 93 units
I didn't bother to calculate TV because we are looking for shortest distance for the trip and by inspection if he goes from T to V first before Point U, it will be a longer journey.
Thus, shortest distance = TU + UV
shortest distance = 72 + 93 = 165 units
read more at; brainly.com/question/1830261
