Answer:
X(−64/3, 0); 8/3
Step-by-step explanation:
To find the coordinates of the point X, 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 JK and JW.
Point J is the origin. Thus, the coordinates of the point J are (0,0).
It is given in the figure that the coordinates of the point K are (0,6).
To find JK, substitute x1=0, x2=0, y1=0, and y2=6 into the distance formula.
JK=(0−0)2+(6−0)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=62‾‾√=6
The length of JK is 6.
It is given in the figure that the coordinates of the point W are (0,16).
To find JW, substitute x1=0, x2=0, y1=0, and y2=16 into the distance formula.
JW=(0−0)2+(16−0)2‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾‾√=162‾‾‾‾√=16
The length of JW is 16.
To determine the scale factor, set up a ratio of the lengths of two corresponding sides, JW and JK, of the triangles.
JWJK=166=83
The scale factor is 83.
To find the coordinates of the point X multiply the coordinates of the point L by the scale factor.
It is given in the figure that the coordinates of the point L are (−8,0).
X(−8⋅83,0⋅83)=X(−643,0)
The coordinates of the point X are (−643,0).
The figure shows the same triangles K J L and W J X as in the beginning of the task. Point X is at minus 64 thirds, zero.
Therefore, the coordinates of X is (−643,0) and the scale factor is 83.