Answer:
K(0, −7.5); 5/8
Explanation:
To find the coordinates of the point K, first find the scale factor for a dilation of two similar triangles in the coordinate plane
To determine the scale factor, set up a ratio of the lengths of two corresponding sides of the triangles.
Use the Distance Formula d=(x2−x1)2+(y2−y1)2−−−−−−−−−−−−−−−−−−√
to find the length of the sides OB and OP.
Point O is the origin. Thus, the coordinates of the point O are (0,0).
It is given in the figure that the coordinates of the point B
are (−4,0).
To find OB, substitute x1=0, x2=5, y1=0, and y2=0 into the distance formula.
OB=(5−0)2+(0−0)2−−−−−−−−−−−−−−−√=52−−√=5
The length of OB is 5.
It is given in the figure that the coordinates of the point P
are (8,0).
To find OP, substitute x1=0, x2=8, y1=0, and y2=0
into the distance formula.
OP=(8−0)2+(0−0)2−−−−−−−−−−−−−−−√=82−−√=8
The length of OP is 8.
To determine the scale factor, set up a ratio of the lengths of two corresponding sides, OB and OP, of the triangles.
OB/OP=58
The scale factor is 5/8.
To find the coordinates of the point K multiply the coordinates of the point S by the scale factor.
It is given in the figure that the coordinates of the point S are (0,−12).
K(0⋅58,−12⋅58)=K(0,−608)=K(0,−152)=K(0,−7.5)
The coordinates of the point K are (0,−7.5).
The figure shows the same triangles P O S and B O K as in the beginning of the task. Point K is at zero, minus 7 point 5.
Therefore, the coordinates of K are (0,−7.5) and the scale factor is 5/8.
