Lisa is writing a coordinate proof to show that the diagonals of a square are perpendicular to each other. she starts by assigni
ng coordinates as given. a square is graphed on a coordinate plane. the horizontal x-axis and y-axis is solid and grid is hidden. the vertices are labeled as k, g, h and j. the vertex labeled as k lies on begin ordered pair 0 comma 0 end ordered pair. the vertex labeled as g lies on begin ordered pair 0 comma a end ordered pair. the vertex labeled as j lies on begin ordered pair a comma 0 end ordered pair. one vertex is unlabeled. diagonal k h and g j are drawn. drag and drop the correct answers to complete the proof. since ghjk is a square, the coordinates of h are (a, ). the slope of kh¯¯¯¯¯¯ is . the slope of is −1 . the product of the slopes of the diagonals is . therefore, kh¯¯¯¯¯¯ is perpendicular to gj¯¯¯¯¯ . 10−1agj¯¯¯¯¯gk¯¯¯¯¯¯
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Answer:
Step-by-step explanation:
We want to reflect this 2x1 vector on the line y = x.
To make this reflection we must use the following matrix:
Where R is known as the reflection matrix on the line x = y
Now perform the product of the vector <-1,5> x R.
The vector matrix that represents the reflection of the vector <-1,5> across the line x = y is: