Find closest value from array data

Hello,

I need to find the closest value from an array data. Using the index match array function the closest value can be found. However in my case, as shown in the example below, I want to find the closest match to column A in sheet 1, from sheet 2; also based on column 2. Example, the closest match to 0, corresponding to A, B, C and D are 0.05, 0.25, 0.3 and 0.4 respectively (Expected Output1). From this output, the final value is looked up from colum C (Expected Output2). If I can get Expected Output1, Expected Output2 is a result of an index match array function. Appreciate your time. Thanks.

Sheet 1:
Column A  Column B  Expected Output1 Expected Output2
0         A         0.05             10
0         B         0.25             30
0         C         0.3              70
0         D         0.4              90

Sheet 2:
Column A  Column B  Column C
0.05      A         10
0.1       A         20
0.25      B         30
0.1       B         40
0.2       B         50
0.3       B         60
0.3       C         70
0.1       C         80
0.4       D         90
0.1       D         100
0.2       D         120
0.3       D         130